TSTP Solution File: DAT027_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT027_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n023.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 : Wed Aug 30 22:18:55 EDT 2023
% Result : Theorem 4.74s 1.30s
% Output : Proof 5.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT027_1 : TPTP v8.1.2. Released v5.0.0.
% 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 14:34:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.57/0.54 ________ _____
% 0.57/0.54 ___ __ \_________(_)________________________________
% 0.57/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.57/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.57/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.57/0.54
% 0.57/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.54 (2023-06-19)
% 0.57/0.54
% 0.57/0.54 (c) Philipp Rümmer, 2009-2023
% 0.57/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.54 Amanda Stjerna.
% 0.57/0.54 Free software under BSD-3-Clause.
% 0.57/0.54
% 0.57/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.54
% 0.57/0.54 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.56 Running up to 7 provers in parallel.
% 0.61/0.57 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.57 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.57 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.57 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/0.95 Prover 1: Preprocessing ...
% 2.44/0.95 Prover 4: Preprocessing ...
% 2.69/1.00 Prover 5: Preprocessing ...
% 2.69/1.00 Prover 2: Preprocessing ...
% 2.69/1.00 Prover 6: Preprocessing ...
% 2.69/1.00 Prover 3: Preprocessing ...
% 2.69/1.00 Prover 0: Preprocessing ...
% 3.84/1.16 Prover 1: Constructing countermodel ...
% 3.84/1.16 Prover 4: Constructing countermodel ...
% 3.84/1.16 Prover 3: Constructing countermodel ...
% 3.84/1.16 Prover 6: Proving ...
% 3.84/1.16 Prover 0: Proving ...
% 3.84/1.16 Prover 2: Proving ...
% 3.84/1.16 Prover 5: Proving ...
% 4.74/1.30 Prover 3: proved (737ms)
% 4.74/1.30
% 4.74/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.74/1.30
% 4.74/1.30 Prover 5: stopped
% 4.74/1.30 Prover 2: stopped
% 4.74/1.30 Prover 0: stopped
% 4.74/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.74/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.74/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.74/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.17/1.33 Prover 6: stopped
% 5.17/1.33 Prover 1: Found proof (size 18)
% 5.17/1.33 Prover 1: proved (757ms)
% 5.17/1.33 Prover 4: Found proof (size 15)
% 5.17/1.33 Prover 4: proved (762ms)
% 5.17/1.34 Prover 10: Preprocessing ...
% 5.17/1.34 Prover 8: Preprocessing ...
% 5.17/1.34 Prover 11: Preprocessing ...
% 5.17/1.34 Prover 7: Preprocessing ...
% 5.17/1.35 Prover 10: stopped
% 5.17/1.35 Prover 7: stopped
% 5.17/1.36 Prover 11: stopped
% 5.45/1.38 Prover 8: Warning: ignoring some quantifiers
% 5.45/1.39 Prover 8: Constructing countermodel ...
% 5.45/1.39 Prover 8: stopped
% 5.45/1.39
% 5.45/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.45/1.39
% 5.45/1.40 % SZS output start Proof for theBenchmark
% 5.45/1.40 Assumptions after simplification:
% 5.45/1.40 ---------------------------------
% 5.45/1.40
% 5.45/1.40 (ax4)
% 5.45/1.42 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 5.45/1.42 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 5.45/1.42 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 5.45/1.42 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 5.45/1.42 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 5.45/1.42 collection(v1) | in(v0, v1) = 0)
% 5.45/1.42
% 5.45/1.42 (ax5)
% 5.45/1.43 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 5.45/1.43 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) =
% 5.45/1.43 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 5.45/1.43 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (
% 5.45/1.43 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | ( ~ (v2
% 5.45/1.43 = v0) & in(v0, v1) = 0))
% 5.45/1.43
% 5.45/1.43 (co1)
% 5.45/1.43 ? [v0: collection] : ? [v1: collection] : ? [v2: int] : ? [v3: int] : ?
% 5.45/1.43 [v4: collection] : ($lesseq(0, v3) & remove(v2, v1) = v4 & add($sum(v3, v2),
% 5.45/1.43 v4) = v0 & in(v2, v1) = 0 & collection(v4) & collection(v1) &
% 5.45/1.43 collection(v0) & ! [v5: int] : ( ~ ($lesseq(v5, 0) | ~ (in(v5, v1) = 0)) &
% 5.45/1.43 ? [v5: int] : ($lesseq(v5, 0)in(v5, v0) = 0))
% 5.45/1.43
% 5.45/1.43 Further assumptions not needed in the proof:
% 5.45/1.43 --------------------------------------------
% 5.45/1.43 ax1, ax2, ax3
% 5.45/1.43
% 5.45/1.43 Those formulas are unsatisfiable:
% 5.45/1.43 ---------------------------------
% 5.45/1.43
% 5.45/1.43 Begin of proof
% 5.45/1.43 |
% 5.45/1.43 | ALPHA: (ax4) implies:
% 5.76/1.43 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 5.76/1.43 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 5.76/1.43 | collection(v1) | in(v0, v1) = 0)
% 5.76/1.44 |
% 5.76/1.44 | ALPHA: (ax5) implies:
% 5.76/1.44 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 5.76/1.44 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) |
% 5.76/1.44 | ( ~ (v2 = v0) & in(v0, v1) = 0))
% 5.76/1.44 |
% 5.76/1.44 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2,
% 5.76/1.44 | all_11_3, all_11_4 gives:
% 5.76/1.44 | (3) $lesseq(0, all_11_1) & remove(all_11_2, all_11_3) = all_11_0 &
% 5.76/1.44 | add($sum(all_11_1, all_11_2), all_11_0) = all_11_4 & in(all_11_2,
% 5.76/1.44 | all_11_3) = 0 & collection(all_11_0) & collection(all_11_3) &
% 5.76/1.44 | collection(all_11_4) & ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0,
% 5.76/1.44 | all_11_3) = 0)) & ? [v0: int] : ($lesseq(v0, 0)in(v0,
% 5.76/1.44 | all_11_4) = 0)
% 5.76/1.44 |
% 5.76/1.44 | ALPHA: (3) implies:
% 5.76/1.44 | (4) $lesseq(0, all_11_1)
% 5.76/1.44 | (5) collection(all_11_3)
% 5.76/1.44 | (6) collection(all_11_0)
% 5.76/1.44 | (7) in(all_11_2, all_11_3) = 0
% 5.76/1.44 | (8) add($sum(all_11_1, all_11_2), all_11_0) = all_11_4
% 5.76/1.44 | (9) remove(all_11_2, all_11_3) = all_11_0
% 5.76/1.44 | (10) ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_3) = 0))
% 5.76/1.44 | (11) ? [v0: int] : ($lesseq(v0, 0)in(v0, all_11_4) = 0)
% 5.76/1.44 |
% 5.76/1.44 | DELTA: instantiating (11) with fresh symbol all_15_0 gives:
% 5.76/1.44 | (12) $lesseq(all_15_0, 0)in(all_15_0, all_11_4) = 0
% 5.76/1.44 |
% 5.76/1.44 | ALPHA: (12) implies:
% 5.76/1.44 | (13) $lesseq(all_15_0, 0)
% 5.76/1.45 | (14) in(all_15_0, all_11_4) = 0
% 5.76/1.45 |
% 5.76/1.45 | GROUND_INST: instantiating (10) with all_11_2, simplifying with (7) gives:
% 5.76/1.45 | (15) $lesseq(1, all_11_2)
% 5.76/1.45 |
% 5.76/1.45 | GROUND_INST: instantiating (1) with all_15_0, all_11_0, $sum(all_11_1,
% 5.76/1.45 | all_11_2), all_11_4, simplifying with (6), (8), (14) gives:
% 5.76/1.45 | (16) $difference(all_15_0, all_11_1) = all_11_2 | in(all_15_0, all_11_0) =
% 5.76/1.45 | 0
% 5.76/1.45 |
% 5.76/1.45 | BETA: splitting (16) gives:
% 5.76/1.45 |
% 5.76/1.45 | Case 1:
% 5.76/1.45 | |
% 5.76/1.45 | | (17) in(all_15_0, all_11_0) = 0
% 5.76/1.45 | |
% 5.76/1.45 | | GROUND_INST: instantiating (2) with all_15_0, all_11_3, all_11_2, all_11_0,
% 5.76/1.45 | | simplifying with (5), (9), (17) gives:
% 5.76/1.45 | | (18) ~ (all_15_0 = all_11_2) & in(all_15_0, all_11_3) = 0
% 5.76/1.45 | |
% 5.76/1.45 | | ALPHA: (18) implies:
% 5.76/1.45 | | (19) in(all_15_0, all_11_3) = 0
% 5.76/1.45 | |
% 5.76/1.45 | | GROUND_INST: instantiating (10) with all_15_0, simplifying with (19) gives:
% 5.76/1.45 | | (20) $lesseq(1, all_15_0)
% 5.76/1.45 | |
% 5.76/1.45 | | COMBINE_INEQS: (13), (20) imply:
% 5.76/1.45 | | (21) $false
% 5.76/1.45 | |
% 5.76/1.45 | | CLOSE: (21) is inconsistent.
% 5.76/1.45 | |
% 5.76/1.45 | Case 2:
% 5.76/1.45 | |
% 5.76/1.45 | | (22) $difference(all_15_0, all_11_1) = all_11_2
% 5.76/1.45 | |
% 5.76/1.45 | | REDUCE: (13), (22) imply:
% 5.76/1.45 | | (23) $lesseq(all_11_2, $product(-1, all_11_1))
% 5.76/1.45 | |
% 5.76/1.45 | | COMBINE_INEQS: (4), (23) imply:
% 5.76/1.45 | | (24) $lesseq(all_11_2, 0)
% 5.76/1.45 | |
% 5.76/1.45 | | COMBINE_INEQS: (15), (24) imply:
% 5.76/1.45 | | (25) $false
% 5.76/1.45 | |
% 5.76/1.45 | | CLOSE: (25) is inconsistent.
% 5.76/1.45 | |
% 5.76/1.45 | End of split
% 5.76/1.45 |
% 5.76/1.45 End of proof
% 5.76/1.45 % SZS output end Proof for theBenchmark
% 5.76/1.45
% 5.76/1.45 909ms
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