TSTP Solution File: SET627+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET627+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n009.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 15:25:43 EDT 2023
% Result : Theorem 3.92s 1.24s
% Output : Proof 5.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET627+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:37:20 EDT 2023
% 0.13/0.34 % 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.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.86/0.93 Prover 1: Preprocessing ...
% 1.86/0.93 Prover 4: Preprocessing ...
% 2.28/0.98 Prover 6: Preprocessing ...
% 2.28/0.98 Prover 0: Preprocessing ...
% 2.28/0.98 Prover 2: Preprocessing ...
% 2.28/0.98 Prover 5: Preprocessing ...
% 2.28/0.98 Prover 3: Preprocessing ...
% 3.17/1.12 Prover 2: Proving ...
% 3.17/1.12 Prover 5: Proving ...
% 3.17/1.12 Prover 6: Proving ...
% 3.43/1.14 Prover 3: Constructing countermodel ...
% 3.43/1.14 Prover 1: Constructing countermodel ...
% 3.43/1.15 Prover 4: Constructing countermodel ...
% 3.43/1.17 Prover 0: Proving ...
% 3.92/1.24 Prover 3: proved (620ms)
% 3.92/1.24
% 3.92/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.92/1.24
% 3.92/1.24 Prover 0: stopped
% 3.92/1.24 Prover 5: stopped
% 3.92/1.24 Prover 2: stopped
% 3.92/1.24 Prover 6: stopped
% 3.92/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.92/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.92/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.92/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.92/1.26 Prover 7: Preprocessing ...
% 3.92/1.26 Prover 8: Preprocessing ...
% 4.37/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.37/1.27 Prover 11: Preprocessing ...
% 4.37/1.28 Prover 13: Preprocessing ...
% 4.37/1.28 Prover 10: Preprocessing ...
% 4.37/1.28 Prover 7: Warning: ignoring some quantifiers
% 4.37/1.29 Prover 7: Constructing countermodel ...
% 4.37/1.31 Prover 13: Warning: ignoring some quantifiers
% 4.37/1.31 Prover 10: Warning: ignoring some quantifiers
% 4.37/1.32 Prover 13: Constructing countermodel ...
% 4.37/1.32 Prover 10: Constructing countermodel ...
% 4.37/1.32 Prover 4: Found proof (size 15)
% 4.37/1.32 Prover 4: proved (708ms)
% 4.37/1.33 Prover 1: Found proof (size 15)
% 4.37/1.33 Prover 1: proved (709ms)
% 4.37/1.33 Prover 10: stopped
% 4.37/1.33 Prover 13: stopped
% 4.37/1.33 Prover 7: stopped
% 4.37/1.33 Prover 8: Warning: ignoring some quantifiers
% 4.37/1.34 Prover 8: Constructing countermodel ...
% 4.37/1.35 Prover 8: stopped
% 4.37/1.35 Prover 11: Constructing countermodel ...
% 4.37/1.36 Prover 11: stopped
% 4.37/1.36
% 4.37/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/1.36
% 4.37/1.36 % SZS output start Proof for theBenchmark
% 4.37/1.36 Assumptions after simplification:
% 4.37/1.36 ---------------------------------
% 4.37/1.36
% 4.37/1.36 (disjoint_defn)
% 5.07/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 5.07/1.40 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : !
% 5.07/1.40 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ $i(v1) |
% 5.07/1.40 ~ $i(v0) | disjoint(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.07/1.40 (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 5.07/1.40 & intersect(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.07/1.40 (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 5.07/1.40 0) & disjoint(v0, v1) = v2))
% 5.07/1.40
% 5.07/1.40 (empty_set_defn)
% 5.07/1.40 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 5.07/1.40
% 5.07/1.40 (intersect_defn)
% 5.07/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 5.07/1.40 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) |
% 5.07/1.40 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0:
% 5.07/1.40 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0,
% 5.07/1.40 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0)
% 5.07/1.40 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : !
% 5.07/1.40 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 5.07/1.40 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 5.07/1.40
% 5.07/1.41 (prove_th104)
% 5.23/1.41 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & disjoint(v0,
% 5.23/1.41 empty_set) = v1 & $i(v0))
% 5.23/1.41
% 5.23/1.41 Further assumptions not needed in the proof:
% 5.23/1.41 --------------------------------------------
% 5.23/1.41 empty_defn, symmetry_of_intersect
% 5.23/1.41
% 5.23/1.41 Those formulas are unsatisfiable:
% 5.23/1.41 ---------------------------------
% 5.23/1.41
% 5.23/1.41 Begin of proof
% 5.23/1.41 |
% 5.23/1.41 | ALPHA: (empty_set_defn) implies:
% 5.23/1.41 | (1) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 5.23/1.41 |
% 5.23/1.41 | ALPHA: (intersect_defn) implies:
% 5.23/1.41 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) |
% 5.23/1.41 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 &
% 5.23/1.41 | $i(v2)))
% 5.23/1.41 |
% 5.23/1.41 | ALPHA: (disjoint_defn) implies:
% 5.23/1.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 5.23/1.41 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0)
% 5.23/1.41 |
% 5.23/1.41 | ALPHA: (prove_th104) implies:
% 5.23/1.41 | (4) $i(empty_set)
% 5.23/1.41 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & disjoint(v0, empty_set) =
% 5.23/1.42 | v1 & $i(v0))
% 5.23/1.42 |
% 5.23/1.42 | DELTA: instantiating (5) with fresh symbols all_9_0, all_9_1 gives:
% 5.23/1.42 | (6) ~ (all_9_0 = 0) & disjoint(all_9_1, empty_set) = all_9_0 & $i(all_9_1)
% 5.23/1.42 |
% 5.23/1.42 | ALPHA: (6) implies:
% 5.23/1.42 | (7) ~ (all_9_0 = 0)
% 5.23/1.42 | (8) $i(all_9_1)
% 5.23/1.42 | (9) disjoint(all_9_1, empty_set) = all_9_0
% 5.23/1.42 |
% 5.23/1.42 | GROUND_INST: instantiating (3) with all_9_1, empty_set, all_9_0, simplifying
% 5.23/1.42 | with (4), (8), (9) gives:
% 5.23/1.42 | (10) all_9_0 = 0 | intersect(all_9_1, empty_set) = 0
% 5.23/1.42 |
% 5.23/1.42 | BETA: splitting (10) gives:
% 5.23/1.42 |
% 5.23/1.42 | Case 1:
% 5.23/1.42 | |
% 5.23/1.42 | | (11) intersect(all_9_1, empty_set) = 0
% 5.23/1.42 | |
% 5.23/1.42 | | GROUND_INST: instantiating (2) with all_9_1, empty_set, simplifying with
% 5.23/1.42 | | (4), (8), (11) gives:
% 5.23/1.42 | | (12) ? [v0: $i] : (member(v0, all_9_1) = 0 & member(v0, empty_set) = 0 &
% 5.23/1.42 | | $i(v0))
% 5.23/1.42 | |
% 5.23/1.42 | | DELTA: instantiating (12) with fresh symbol all_24_0 gives:
% 5.23/1.42 | | (13) member(all_24_0, all_9_1) = 0 & member(all_24_0, empty_set) = 0 &
% 5.23/1.42 | | $i(all_24_0)
% 5.23/1.42 | |
% 5.23/1.42 | | ALPHA: (13) implies:
% 5.23/1.42 | | (14) $i(all_24_0)
% 5.23/1.42 | | (15) member(all_24_0, empty_set) = 0
% 5.23/1.42 | |
% 5.23/1.42 | | GROUND_INST: instantiating (1) with all_24_0, simplifying with (14), (15)
% 5.23/1.42 | | gives:
% 5.23/1.42 | | (16) $false
% 5.23/1.42 | |
% 5.23/1.42 | | CLOSE: (16) is inconsistent.
% 5.23/1.42 | |
% 5.23/1.42 | Case 2:
% 5.23/1.42 | |
% 5.23/1.43 | | (17) all_9_0 = 0
% 5.23/1.43 | |
% 5.23/1.43 | | REDUCE: (7), (17) imply:
% 5.23/1.43 | | (18) $false
% 5.23/1.43 | |
% 5.23/1.43 | | CLOSE: (18) is inconsistent.
% 5.23/1.43 | |
% 5.23/1.43 | End of split
% 5.23/1.43 |
% 5.23/1.43 End of proof
% 5.23/1.43 % SZS output end Proof for theBenchmark
% 5.23/1.43
% 5.23/1.43 828ms
%------------------------------------------------------------------------------