TSTP Solution File: SET062+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET062+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 15:23:29 EDT 2023
% Result : Theorem 7.31s 1.78s
% Output : Proof 8.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET062+4 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n001.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 : Sat Aug 26 12:25:00 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.58 ________ _____
% 0.18/0.58 ___ __ \_________(_)________________________________
% 0.18/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.58 (2023-06-19)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2023
% 0.18/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.58 Amanda Stjerna.
% 0.18/0.58 Free software under BSD-3-Clause.
% 0.18/0.58
% 0.18/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.65/1.09 Prover 4: Preprocessing ...
% 2.65/1.09 Prover 1: Preprocessing ...
% 3.03/1.15 Prover 6: Preprocessing ...
% 3.03/1.15 Prover 0: Preprocessing ...
% 3.03/1.15 Prover 2: Preprocessing ...
% 3.03/1.15 Prover 5: Preprocessing ...
% 3.03/1.15 Prover 3: Preprocessing ...
% 5.62/1.62 Prover 3: Constructing countermodel ...
% 6.27/1.63 Prover 6: Proving ...
% 6.27/1.64 Prover 5: Proving ...
% 6.27/1.65 Prover 1: Constructing countermodel ...
% 6.70/1.69 Prover 2: Proving ...
% 6.70/1.69 Prover 4: Constructing countermodel ...
% 7.31/1.78 Prover 3: proved (1160ms)
% 7.31/1.78
% 7.31/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.31/1.78
% 7.31/1.78 Prover 6: stopped
% 7.31/1.78 Prover 2: stopped
% 7.31/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.31/1.78 Prover 0: Proving ...
% 7.31/1.79 Prover 0: stopped
% 7.31/1.79 Prover 5: stopped
% 7.31/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.31/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.31/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.53/1.82 Prover 1: Found proof (size 13)
% 7.53/1.82 Prover 1: proved (1204ms)
% 7.53/1.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.53/1.82 Prover 4: stopped
% 7.69/1.86 Prover 11: Preprocessing ...
% 7.69/1.86 Prover 7: Preprocessing ...
% 7.69/1.86 Prover 8: Preprocessing ...
% 7.69/1.86 Prover 10: Preprocessing ...
% 7.69/1.86 Prover 13: Preprocessing ...
% 7.69/1.88 Prover 7: stopped
% 7.69/1.89 Prover 10: stopped
% 7.69/1.91 Prover 11: stopped
% 7.69/1.91 Prover 13: stopped
% 8.32/2.00 Prover 8: Warning: ignoring some quantifiers
% 8.32/2.01 Prover 8: Constructing countermodel ...
% 8.32/2.02 Prover 8: stopped
% 8.32/2.02
% 8.32/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.32/2.02
% 8.32/2.03 % SZS output start Proof for theBenchmark
% 8.32/2.03 Assumptions after simplification:
% 8.32/2.03 ---------------------------------
% 8.32/2.03
% 8.32/2.03 (empty_set)
% 8.32/2.08 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 8.32/2.08
% 8.32/2.08 (subset)
% 8.32/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 8.32/2.08 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 8.32/2.08 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 8.32/2.08 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 8.32/2.08 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 8.32/2.08
% 8.32/2.09 (thI15)
% 8.32/2.09 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set,
% 8.32/2.09 v0) = v1 & $i(v0))
% 8.32/2.09
% 8.32/2.09 Further assumptions not needed in the proof:
% 8.32/2.09 --------------------------------------------
% 8.32/2.09 difference, equal_set, intersection, power_set, product, singleton, sum, union,
% 8.32/2.09 unordered_pair
% 8.32/2.09
% 8.32/2.09 Those formulas are unsatisfiable:
% 8.32/2.09 ---------------------------------
% 8.32/2.09
% 8.32/2.09 Begin of proof
% 8.32/2.09 |
% 8.32/2.10 | ALPHA: (subset) implies:
% 8.32/2.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 8.32/2.10 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 8.32/2.10 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 8.32/2.10 |
% 8.32/2.10 | ALPHA: (empty_set) implies:
% 8.32/2.10 | (2) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 8.32/2.10 |
% 8.32/2.10 | ALPHA: (thI15) implies:
% 8.32/2.10 | (3) $i(empty_set)
% 8.32/2.10 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set, v0) = v1
% 8.32/2.10 | & $i(v0))
% 8.32/2.10 |
% 8.32/2.10 | DELTA: instantiating (4) with fresh symbols all_15_0, all_15_1 gives:
% 8.32/2.11 | (5) ~ (all_15_0 = 0) & subset(empty_set, all_15_1) = all_15_0 &
% 8.32/2.11 | $i(all_15_1)
% 8.32/2.11 |
% 8.32/2.11 | ALPHA: (5) implies:
% 8.32/2.11 | (6) ~ (all_15_0 = 0)
% 8.32/2.11 | (7) $i(all_15_1)
% 8.32/2.11 | (8) subset(empty_set, all_15_1) = all_15_0
% 8.32/2.11 |
% 8.32/2.11 | GROUND_INST: instantiating (1) with empty_set, all_15_1, all_15_0, simplifying
% 8.32/2.11 | with (3), (7), (8) gives:
% 8.32/2.11 | (9) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 8.32/2.11 | all_15_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 8.32/2.12 |
% 8.32/2.12 | BETA: splitting (9) gives:
% 8.32/2.12 |
% 8.32/2.12 | Case 1:
% 8.32/2.12 | |
% 8.32/2.12 | | (10) all_15_0 = 0
% 8.32/2.12 | |
% 8.32/2.12 | | REDUCE: (6), (10) imply:
% 8.32/2.12 | | (11) $false
% 8.32/2.12 | |
% 8.32/2.12 | | CLOSE: (11) is inconsistent.
% 8.32/2.12 | |
% 8.32/2.12 | Case 2:
% 8.32/2.12 | |
% 8.32/2.13 | | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) =
% 8.32/2.13 | | v1 & member(v0, empty_set) = 0 & $i(v0))
% 8.32/2.13 | |
% 8.32/2.13 | | DELTA: instantiating (12) with fresh symbols all_24_0, all_24_1 gives:
% 8.32/2.13 | | (13) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = all_24_0 &
% 8.32/2.13 | | member(all_24_1, empty_set) = 0 & $i(all_24_1)
% 8.32/2.13 | |
% 8.32/2.13 | | ALPHA: (13) implies:
% 8.32/2.13 | | (14) $i(all_24_1)
% 8.32/2.13 | | (15) member(all_24_1, empty_set) = 0
% 8.32/2.14 | |
% 8.32/2.14 | | GROUND_INST: instantiating (2) with all_24_1, simplifying with (14), (15)
% 8.32/2.14 | | gives:
% 8.32/2.14 | | (16) $false
% 8.32/2.14 | |
% 8.32/2.14 | | CLOSE: (16) is inconsistent.
% 8.32/2.14 | |
% 8.32/2.14 | End of split
% 8.32/2.14 |
% 8.32/2.14 End of proof
% 8.32/2.14 % SZS output end Proof for theBenchmark
% 8.32/2.14
% 8.32/2.14 1554ms
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