TSTP Solution File: SET604+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET604+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 : n010.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 15:25:33 EDT 2023
% Result : Theorem 4.62s 1.33s
% Output : Proof 5.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 12:23:04 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
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 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 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 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 1.81/0.95 Prover 4: Preprocessing ...
% 1.81/0.95 Prover 1: Preprocessing ...
% 1.81/0.99 Prover 0: Preprocessing ...
% 1.81/0.99 Prover 6: Preprocessing ...
% 1.81/0.99 Prover 5: Preprocessing ...
% 1.81/0.99 Prover 2: Preprocessing ...
% 1.81/0.99 Prover 3: Preprocessing ...
% 3.82/1.20 Prover 5: Proving ...
% 3.90/1.20 Prover 2: Proving ...
% 3.90/1.21 Prover 6: Proving ...
% 3.90/1.21 Prover 3: Constructing countermodel ...
% 3.90/1.21 Prover 1: Constructing countermodel ...
% 3.90/1.23 Prover 0: Proving ...
% 3.90/1.25 Prover 4: Constructing countermodel ...
% 4.62/1.33 Prover 3: proved (705ms)
% 4.62/1.33
% 4.62/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/1.33
% 4.62/1.34 Prover 5: stopped
% 4.62/1.34 Prover 2: stopped
% 4.62/1.34 Prover 6: stopped
% 4.62/1.34 Prover 0: stopped
% 4.62/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.62/1.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.62/1.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.62/1.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.62/1.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.62/1.36 Prover 7: Preprocessing ...
% 4.62/1.36 Prover 8: Preprocessing ...
% 4.62/1.36 Prover 10: Preprocessing ...
% 4.62/1.38 Prover 13: Preprocessing ...
% 4.62/1.38 Prover 11: Preprocessing ...
% 4.62/1.39 Prover 1: Found proof (size 14)
% 4.62/1.39 Prover 4: Found proof (size 14)
% 4.62/1.39 Prover 1: proved (765ms)
% 4.62/1.39 Prover 4: proved (752ms)
% 4.62/1.40 Prover 7: Warning: ignoring some quantifiers
% 4.62/1.40 Prover 13: stopped
% 4.62/1.41 Prover 11: stopped
% 4.62/1.41 Prover 10: Warning: ignoring some quantifiers
% 4.62/1.41 Prover 7: Constructing countermodel ...
% 4.62/1.41 Prover 10: Constructing countermodel ...
% 4.62/1.42 Prover 7: stopped
% 4.62/1.42 Prover 10: stopped
% 5.29/1.43 Prover 8: Warning: ignoring some quantifiers
% 5.29/1.43 Prover 8: Constructing countermodel ...
% 5.29/1.44 Prover 8: stopped
% 5.29/1.44
% 5.29/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/1.44
% 5.29/1.44 % SZS output start Proof for theBenchmark
% 5.29/1.45 Assumptions after simplification:
% 5.29/1.45 ---------------------------------
% 5.29/1.45
% 5.29/1.45 (difference_empty_set)
% 5.29/1.48 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.29/1.48 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 5.29/1.48 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.29/1.48 (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) =
% 5.29/1.48 0)
% 5.29/1.48
% 5.29/1.48 (empty_set_subset)
% 5.29/1.48 $i(empty_set) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set,
% 5.29/1.48 v0) = v1) | ~ $i(v0))
% 5.29/1.48
% 5.29/1.48 (prove_no_difference_with_empty_set)
% 5.29/1.48 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 5.29/1.48 difference(empty_set, v0) = v1 & $i(v1) & $i(v0))
% 5.29/1.48
% 5.29/1.48 Further assumptions not needed in the proof:
% 5.29/1.48 --------------------------------------------
% 5.29/1.48 difference_defn, empty_defn, empty_set_defn, equal_defn, reflexivity_of_subset,
% 5.29/1.48 subset_defn
% 5.29/1.48
% 5.29/1.48 Those formulas are unsatisfiable:
% 5.29/1.48 ---------------------------------
% 5.29/1.48
% 5.29/1.48 Begin of proof
% 5.29/1.48 |
% 5.29/1.48 | ALPHA: (empty_set_subset) implies:
% 5.29/1.48 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)
% 5.29/1.48 | | ~ $i(v0))
% 5.29/1.48 |
% 5.29/1.48 | ALPHA: (difference_empty_set) implies:
% 5.29/1.49 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.29/1.49 | (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 5.29/1.49 | ~ (v3 = 0) & subset(v0, v1) = v3))
% 5.29/1.49 |
% 5.29/1.49 | ALPHA: (prove_no_difference_with_empty_set) implies:
% 5.29/1.49 | (3) $i(empty_set)
% 5.29/1.49 | (4) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 5.29/1.49 | difference(empty_set, v0) = v1 & $i(v1) & $i(v0))
% 5.29/1.49 |
% 5.29/1.49 | DELTA: instantiating (4) with fresh symbols all_12_0, all_12_1 gives:
% 5.29/1.49 | (5) ~ (all_12_0 = empty_set) & difference(empty_set, all_12_1) = all_12_0
% 5.29/1.49 | & $i(all_12_0) & $i(all_12_1)
% 5.29/1.49 |
% 5.29/1.49 | ALPHA: (5) implies:
% 5.29/1.49 | (6) ~ (all_12_0 = empty_set)
% 5.29/1.49 | (7) $i(all_12_1)
% 5.29/1.49 | (8) difference(empty_set, all_12_1) = all_12_0
% 5.29/1.49 |
% 5.29/1.49 | GROUND_INST: instantiating (2) with empty_set, all_12_1, all_12_0, simplifying
% 5.29/1.49 | with (3), (7), (8) gives:
% 5.29/1.49 | (9) all_12_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set,
% 5.29/1.49 | all_12_1) = v0)
% 5.29/1.49 |
% 5.29/1.49 | BETA: splitting (9) gives:
% 5.29/1.49 |
% 5.29/1.49 | Case 1:
% 5.29/1.49 | |
% 5.29/1.49 | | (10) all_12_0 = empty_set
% 5.29/1.49 | |
% 5.29/1.49 | | REDUCE: (6), (10) imply:
% 5.29/1.49 | | (11) $false
% 5.29/1.49 | |
% 5.29/1.49 | | CLOSE: (11) is inconsistent.
% 5.29/1.49 | |
% 5.29/1.49 | Case 2:
% 5.29/1.49 | |
% 5.29/1.50 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(empty_set, all_12_1) = v0)
% 5.29/1.50 | |
% 5.29/1.50 | | DELTA: instantiating (12) with fresh symbol all_21_0 gives:
% 5.29/1.50 | | (13) ~ (all_21_0 = 0) & subset(empty_set, all_12_1) = all_21_0
% 5.29/1.50 | |
% 5.29/1.50 | | ALPHA: (13) implies:
% 5.29/1.50 | | (14) ~ (all_21_0 = 0)
% 5.29/1.50 | | (15) subset(empty_set, all_12_1) = all_21_0
% 5.29/1.50 | |
% 5.29/1.50 | | GROUND_INST: instantiating (1) with all_12_1, all_21_0, simplifying with
% 5.29/1.50 | | (7), (15) gives:
% 5.29/1.50 | | (16) all_21_0 = 0
% 5.29/1.50 | |
% 5.29/1.50 | | REDUCE: (14), (16) imply:
% 5.29/1.50 | | (17) $false
% 5.29/1.50 | |
% 5.29/1.50 | | CLOSE: (17) is inconsistent.
% 5.29/1.50 | |
% 5.29/1.50 | End of split
% 5.29/1.50 |
% 5.29/1.50 End of proof
% 5.29/1.50 % SZS output end Proof for theBenchmark
% 5.29/1.50
% 5.29/1.50 892ms
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