TSTP Solution File: SET602+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET602+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 : n011.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 15:25:32 EDT 2023
% Result : Theorem 4.37s 1.40s
% Output : Proof 5.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET602+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 09:43:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.79/1.03 Prover 1: Preprocessing ...
% 1.79/1.03 Prover 4: Preprocessing ...
% 2.37/1.07 Prover 3: Preprocessing ...
% 2.37/1.07 Prover 5: Preprocessing ...
% 2.37/1.07 Prover 6: Preprocessing ...
% 2.37/1.08 Prover 2: Preprocessing ...
% 2.37/1.08 Prover 0: Preprocessing ...
% 3.04/1.28 Prover 1: Constructing countermodel ...
% 3.85/1.29 Prover 5: Proving ...
% 3.85/1.30 Prover 2: Proving ...
% 3.85/1.30 Prover 6: Proving ...
% 3.85/1.31 Prover 3: Constructing countermodel ...
% 3.85/1.32 Prover 4: Constructing countermodel ...
% 3.85/1.33 Prover 0: Proving ...
% 4.37/1.40 Prover 6: proved (719ms)
% 4.37/1.40
% 4.37/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/1.40
% 4.37/1.40 Prover 5: stopped
% 4.37/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.37/1.40 Prover 0: proved (731ms)
% 4.37/1.40
% 4.37/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.37/1.40
% 4.37/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.37/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.37/1.41 Prover 2: stopped
% 4.37/1.42 Prover 3: proved (744ms)
% 4.37/1.42
% 4.95/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.95/1.42
% 4.95/1.43 Prover 8: Preprocessing ...
% 4.95/1.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.95/1.43 Prover 1: Found proof (size 14)
% 4.95/1.43 Prover 1: proved (751ms)
% 4.95/1.43 Prover 7: Preprocessing ...
% 4.95/1.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.95/1.43 Prover 10: Preprocessing ...
% 4.95/1.43 Prover 11: Preprocessing ...
% 4.95/1.43 Prover 4: stopped
% 4.95/1.44 Prover 7: stopped
% 4.95/1.45 Prover 13: Preprocessing ...
% 4.95/1.45 Prover 10: stopped
% 4.95/1.46 Prover 11: stopped
% 4.95/1.46 Prover 13: stopped
% 5.33/1.49 Prover 8: Warning: ignoring some quantifiers
% 5.33/1.49 Prover 8: Constructing countermodel ...
% 5.33/1.50 Prover 8: stopped
% 5.33/1.50
% 5.33/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.33/1.50
% 5.33/1.50 % SZS output start Proof for theBenchmark
% 5.33/1.50 Assumptions after simplification:
% 5.33/1.50 ---------------------------------
% 5.33/1.50
% 5.33/1.50 (difference_empty_set)
% 5.33/1.53 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.33/1.53 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 5.33/1.53 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 5.33/1.53 (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) =
% 5.33/1.53 0)
% 5.33/1.53
% 5.33/1.53 (equal_defn)
% 5.33/1.53 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) |
% 5.33/1.53 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i]
% 5.33/1.53 : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 5.33/1.53
% 5.33/1.53 (prove_self_difference_is_empty_set)
% 5.33/1.53 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 5.33/1.54 difference(v0, v0) = v1 & $i(v1) & $i(v0))
% 5.33/1.54
% 5.33/1.54 Further assumptions not needed in the proof:
% 5.33/1.54 --------------------------------------------
% 5.33/1.54 difference_defn, empty_defn, empty_set_defn, reflexivity_of_subset, subset_defn
% 5.33/1.54
% 5.33/1.54 Those formulas are unsatisfiable:
% 5.33/1.54 ---------------------------------
% 5.33/1.54
% 5.33/1.54 Begin of proof
% 5.33/1.54 |
% 5.33/1.54 | ALPHA: (difference_empty_set) implies:
% 5.33/1.54 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 5.33/1.54 | (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 5.33/1.54 | ~ (v3 = 0) & subset(v0, v1) = v3))
% 5.33/1.54 |
% 5.33/1.54 | ALPHA: (equal_defn) implies:
% 5.33/1.54 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~
% 5.33/1.54 | $i(v0))
% 5.33/1.54 |
% 5.33/1.54 | ALPHA: (prove_self_difference_is_empty_set) implies:
% 5.33/1.54 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) & difference(v0, v0) =
% 5.33/1.54 | v1 & $i(v1) & $i(v0))
% 5.33/1.54 |
% 5.33/1.54 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1 gives:
% 5.33/1.54 | (4) ~ (all_11_0 = empty_set) & difference(all_11_1, all_11_1) = all_11_0 &
% 5.33/1.54 | $i(all_11_0) & $i(all_11_1)
% 5.33/1.54 |
% 5.33/1.54 | ALPHA: (4) implies:
% 5.33/1.54 | (5) ~ (all_11_0 = empty_set)
% 5.33/1.54 | (6) $i(all_11_1)
% 5.33/1.54 | (7) difference(all_11_1, all_11_1) = all_11_0
% 5.33/1.54 |
% 5.33/1.55 | GROUND_INST: instantiating (1) with all_11_1, all_11_1, all_11_0, simplifying
% 5.33/1.55 | with (6), (7) gives:
% 5.33/1.55 | (8) all_11_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_1,
% 5.33/1.55 | all_11_1) = v0)
% 5.33/1.55 |
% 5.33/1.55 | BETA: splitting (8) gives:
% 5.33/1.55 |
% 5.33/1.55 | Case 1:
% 5.33/1.55 | |
% 5.33/1.55 | | (9) all_11_0 = empty_set
% 5.33/1.55 | |
% 5.33/1.55 | | REDUCE: (5), (9) imply:
% 5.33/1.55 | | (10) $false
% 5.33/1.55 | |
% 5.33/1.55 | | CLOSE: (10) is inconsistent.
% 5.33/1.55 | |
% 5.33/1.55 | Case 2:
% 5.33/1.55 | |
% 5.33/1.55 | | (11) ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_1, all_11_1) = v0)
% 5.33/1.55 | |
% 5.33/1.55 | | DELTA: instantiating (11) with fresh symbol all_20_0 gives:
% 5.33/1.55 | | (12) ~ (all_20_0 = 0) & subset(all_11_1, all_11_1) = all_20_0
% 5.33/1.55 | |
% 5.33/1.55 | | ALPHA: (12) implies:
% 5.33/1.55 | | (13) ~ (all_20_0 = 0)
% 5.33/1.55 | | (14) subset(all_11_1, all_11_1) = all_20_0
% 5.33/1.55 | |
% 5.33/1.55 | | GROUND_INST: instantiating (2) with all_11_1, all_20_0, simplifying with
% 5.33/1.55 | | (6), (14) gives:
% 5.33/1.55 | | (15) all_20_0 = 0
% 5.33/1.55 | |
% 5.33/1.55 | | REDUCE: (13), (15) imply:
% 5.33/1.55 | | (16) $false
% 5.33/1.55 | |
% 5.33/1.55 | | CLOSE: (16) is inconsistent.
% 5.33/1.55 | |
% 5.33/1.55 | End of split
% 5.33/1.55 |
% 5.33/1.55 End of proof
% 5.33/1.55 % SZS output end Proof for theBenchmark
% 5.33/1.55
% 5.33/1.55 898ms
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