TSTP Solution File: SET062+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET062+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 : n020.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 2.95s 1.16s
% Output : Proof 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET062+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n020.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 12:12:15 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.91/0.92 Prover 4: Preprocessing ...
% 1.91/0.92 Prover 1: Preprocessing ...
% 1.94/0.98 Prover 6: Preprocessing ...
% 1.94/0.98 Prover 3: Preprocessing ...
% 1.94/0.98 Prover 2: Preprocessing ...
% 1.94/0.98 Prover 5: Preprocessing ...
% 1.94/0.99 Prover 0: Preprocessing ...
% 2.43/1.07 Prover 2: Proving ...
% 2.43/1.07 Prover 5: Proving ...
% 2.43/1.07 Prover 1: Constructing countermodel ...
% 2.43/1.07 Prover 4: Constructing countermodel ...
% 2.95/1.08 Prover 6: Proving ...
% 2.95/1.08 Prover 0: Proving ...
% 2.95/1.08 Prover 3: Constructing countermodel ...
% 2.95/1.16 Prover 3: proved (535ms)
% 2.95/1.16
% 2.95/1.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/1.16
% 2.95/1.16 Prover 0: stopped
% 2.95/1.16 Prover 2: stopped
% 2.95/1.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.95/1.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.95/1.16 Prover 5: stopped
% 2.95/1.16 Prover 6: stopped
% 2.95/1.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.95/1.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.95/1.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.65/1.17 Prover 8: Preprocessing ...
% 3.65/1.17 Prover 10: Preprocessing ...
% 3.65/1.18 Prover 13: Preprocessing ...
% 3.65/1.18 Prover 11: Preprocessing ...
% 3.65/1.18 Prover 7: Preprocessing ...
% 3.80/1.19 Prover 4: Found proof (size 13)
% 3.80/1.19 Prover 4: proved (567ms)
% 3.80/1.19 Prover 1: Found proof (size 13)
% 3.80/1.19 Prover 1: proved (581ms)
% 3.80/1.20 Prover 10: Warning: ignoring some quantifiers
% 3.80/1.20 Prover 13: Warning: ignoring some quantifiers
% 3.80/1.20 Prover 10: Constructing countermodel ...
% 3.80/1.21 Prover 7: Warning: ignoring some quantifiers
% 3.80/1.21 Prover 10: stopped
% 3.80/1.21 Prover 7: Constructing countermodel ...
% 3.80/1.21 Prover 11: stopped
% 3.80/1.21 Prover 7: stopped
% 3.80/1.22 Prover 13: Constructing countermodel ...
% 3.99/1.22 Prover 13: stopped
% 4.02/1.23 Prover 8: Warning: ignoring some quantifiers
% 4.02/1.24 Prover 8: Constructing countermodel ...
% 4.02/1.24 Prover 8: stopped
% 4.02/1.24
% 4.02/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/1.24
% 4.02/1.25 % SZS output start Proof for theBenchmark
% 4.02/1.25 Assumptions after simplification:
% 4.02/1.25 ---------------------------------
% 4.02/1.25
% 4.02/1.25 (empty_set_defn)
% 4.02/1.28 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 4.02/1.28
% 4.02/1.28 (prove_empty_set_subset)
% 4.02/1.28 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set,
% 4.02/1.28 v0) = v1 & $i(v0))
% 4.02/1.28
% 4.02/1.28 (subset_defn)
% 4.02/1.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.02/1.29 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.02/1.29 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 4.02/1.29 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 4.02/1.29 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 4.02/1.29 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 4.02/1.29 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 4.02/1.29 ~ $i(v0) | member(v2, v1) = 0)
% 4.02/1.29
% 4.02/1.29 Further assumptions not needed in the proof:
% 4.02/1.29 --------------------------------------------
% 4.02/1.29 empty_defn, reflexivity_of_subset
% 4.02/1.29
% 4.02/1.29 Those formulas are unsatisfiable:
% 4.02/1.29 ---------------------------------
% 4.02/1.29
% 4.02/1.29 Begin of proof
% 4.02/1.29 |
% 4.02/1.29 | ALPHA: (empty_set_defn) implies:
% 4.02/1.29 | (1) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0))
% 4.02/1.29 |
% 4.02/1.29 | ALPHA: (subset_defn) implies:
% 4.02/1.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.02/1.29 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.02/1.29 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 4.02/1.29 |
% 4.02/1.29 | ALPHA: (prove_empty_set_subset) implies:
% 4.02/1.29 | (3) $i(empty_set)
% 4.02/1.29 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(empty_set, v0) = v1
% 4.02/1.29 | & $i(v0))
% 4.02/1.29 |
% 4.02/1.30 | DELTA: instantiating (4) with fresh symbols all_8_0, all_8_1 gives:
% 4.02/1.30 | (5) ~ (all_8_0 = 0) & subset(empty_set, all_8_1) = all_8_0 & $i(all_8_1)
% 4.02/1.30 |
% 4.02/1.30 | ALPHA: (5) implies:
% 4.02/1.30 | (6) ~ (all_8_0 = 0)
% 4.02/1.30 | (7) $i(all_8_1)
% 4.02/1.30 | (8) subset(empty_set, all_8_1) = all_8_0
% 4.02/1.30 |
% 4.02/1.30 | GROUND_INST: instantiating (2) with empty_set, all_8_1, all_8_0, simplifying
% 4.02/1.30 | with (3), (7), (8) gives:
% 4.02/1.30 | (9) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 4.02/1.30 | all_8_1) = v1 & member(v0, empty_set) = 0 & $i(v0))
% 4.02/1.30 |
% 4.02/1.30 | BETA: splitting (9) gives:
% 4.02/1.30 |
% 4.02/1.30 | Case 1:
% 4.02/1.30 | |
% 4.02/1.30 | | (10) all_8_0 = 0
% 4.02/1.30 | |
% 4.02/1.30 | | REDUCE: (6), (10) imply:
% 4.02/1.30 | | (11) $false
% 4.02/1.30 | |
% 4.02/1.30 | | CLOSE: (11) is inconsistent.
% 4.02/1.30 | |
% 4.02/1.30 | Case 2:
% 4.02/1.30 | |
% 4.02/1.31 | | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1
% 4.02/1.31 | | & member(v0, empty_set) = 0 & $i(v0))
% 4.02/1.31 | |
% 4.02/1.31 | | DELTA: instantiating (12) with fresh symbols all_17_0, all_17_1 gives:
% 4.02/1.31 | | (13) ~ (all_17_0 = 0) & member(all_17_1, all_8_1) = all_17_0 &
% 4.02/1.31 | | member(all_17_1, empty_set) = 0 & $i(all_17_1)
% 4.02/1.31 | |
% 4.02/1.31 | | ALPHA: (13) implies:
% 4.02/1.31 | | (14) $i(all_17_1)
% 4.02/1.31 | | (15) member(all_17_1, empty_set) = 0
% 4.02/1.31 | |
% 4.02/1.31 | | GROUND_INST: instantiating (1) with all_17_1, simplifying with (14), (15)
% 4.02/1.31 | | gives:
% 4.02/1.31 | | (16) $false
% 4.02/1.31 | |
% 4.02/1.31 | | CLOSE: (16) is inconsistent.
% 4.02/1.31 | |
% 4.02/1.31 | End of split
% 4.02/1.31 |
% 4.02/1.31 End of proof
% 4.02/1.31 % SZS output end Proof for theBenchmark
% 4.02/1.31
% 4.02/1.31 713ms
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