TSTP Solution File: SET592+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET592+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 15:25:27 EDT 2023
% Result : Theorem 5.35s 1.44s
% Output : Proof 7.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET592+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 11:40:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.49/0.60 ________ _____
% 0.49/0.60 ___ __ \_________(_)________________________________
% 0.49/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.49/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.49/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.49/0.60
% 0.49/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.49/0.60 (2023-06-19)
% 0.49/0.60
% 0.49/0.60 (c) Philipp Rümmer, 2009-2023
% 0.49/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.49/0.60 Amanda Stjerna.
% 0.49/0.60 Free software under BSD-3-Clause.
% 0.49/0.60
% 0.49/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.49/0.60
% 0.49/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.49/0.62 Running up to 7 provers in parallel.
% 0.49/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.49/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.49/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.49/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.49/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.49/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.49/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.09/0.97 Prover 4: Preprocessing ...
% 2.09/0.97 Prover 1: Preprocessing ...
% 2.47/1.01 Prover 0: Preprocessing ...
% 2.47/1.01 Prover 5: Preprocessing ...
% 2.47/1.01 Prover 3: Preprocessing ...
% 2.47/1.01 Prover 6: Preprocessing ...
% 2.47/1.01 Prover 2: Preprocessing ...
% 4.03/1.26 Prover 3: Warning: ignoring some quantifiers
% 4.35/1.30 Prover 5: Proving ...
% 4.35/1.30 Prover 6: Proving ...
% 4.35/1.30 Prover 3: Constructing countermodel ...
% 4.35/1.30 Prover 2: Proving ...
% 4.35/1.30 Prover 1: Warning: ignoring some quantifiers
% 4.35/1.31 Prover 0: Proving ...
% 4.35/1.31 Prover 1: Constructing countermodel ...
% 4.35/1.32 Prover 4: Warning: ignoring some quantifiers
% 4.35/1.33 Prover 4: Constructing countermodel ...
% 5.35/1.44 Prover 5: proved (816ms)
% 5.35/1.44
% 5.35/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/1.44
% 5.35/1.44 Prover 3: stopped
% 5.35/1.45 Prover 2: stopped
% 5.35/1.45 Prover 6: stopped
% 5.68/1.46 Prover 0: stopped
% 5.68/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.68/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.68/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.68/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.68/1.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.68/1.48 Prover 7: Preprocessing ...
% 5.68/1.48 Prover 10: Preprocessing ...
% 5.68/1.48 Prover 8: Preprocessing ...
% 5.68/1.48 Prover 11: Preprocessing ...
% 5.68/1.49 Prover 13: Preprocessing ...
% 5.68/1.51 Prover 4: gave up
% 5.68/1.52 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.68/1.52 Prover 1: gave up
% 5.68/1.53 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.68/1.54 Prover 7: Warning: ignoring some quantifiers
% 6.33/1.54 Prover 10: Warning: ignoring some quantifiers
% 6.33/1.54 Prover 19: Preprocessing ...
% 6.33/1.54 Prover 16: Preprocessing ...
% 6.33/1.54 Prover 10: Constructing countermodel ...
% 6.33/1.56 Prover 7: Constructing countermodel ...
% 6.33/1.56 Prover 13: Warning: ignoring some quantifiers
% 6.33/1.57 Prover 13: Constructing countermodel ...
% 6.33/1.58 Prover 11: Warning: ignoring some quantifiers
% 6.59/1.59 Prover 11: Constructing countermodel ...
% 6.59/1.59 Prover 10: Found proof (size 8)
% 6.59/1.59 Prover 10: proved (136ms)
% 6.59/1.59 Prover 7: stopped
% 6.59/1.59 Prover 13: stopped
% 6.59/1.59 Prover 8: Warning: ignoring some quantifiers
% 6.59/1.59 Prover 16: Warning: ignoring some quantifiers
% 6.59/1.59 Prover 11: stopped
% 6.59/1.60 Prover 8: Constructing countermodel ...
% 6.59/1.60 Prover 16: Constructing countermodel ...
% 6.59/1.60 Prover 8: stopped
% 6.59/1.60 Prover 16: stopped
% 6.59/1.63 Prover 19: Warning: ignoring some quantifiers
% 6.59/1.63 Prover 19: Constructing countermodel ...
% 6.59/1.64 Prover 19: stopped
% 6.59/1.64
% 6.59/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.59/1.64
% 6.59/1.64 % SZS output start Proof for theBenchmark
% 6.59/1.64 Assumptions after simplification:
% 6.59/1.64 ---------------------------------
% 6.59/1.64
% 6.59/1.64 (intersection_of_subsets)
% 7.06/1.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1,
% 7.06/1.67 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v2) | ~
% 7.06/1.67 subset(v0, v1) | subset(v0, v3))
% 7.06/1.67
% 7.06/1.67 (prove_th51)
% 7.06/1.67 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set)
% 7.06/1.67 & intersection(v1, v2) = empty_set & $i(v2) & $i(v1) & $i(v0) & subset(v0,
% 7.06/1.67 v2) & subset(v0, v1))
% 7.06/1.67
% 7.06/1.67 (subset_of_empty_set_is_empty_set)
% 7.06/1.67 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0,
% 7.06/1.67 empty_set))
% 7.06/1.67
% 7.06/1.67 Further assumptions not needed in the proof:
% 7.06/1.67 --------------------------------------------
% 7.06/1.67 commutativity_of_intersection, empty_defn, empty_set_defn, equal_defn,
% 7.06/1.67 equal_member_defn, intersection_defn, reflexivity_of_subset, subset_defn
% 7.06/1.67
% 7.06/1.67 Those formulas are unsatisfiable:
% 7.06/1.67 ---------------------------------
% 7.06/1.67
% 7.06/1.67 Begin of proof
% 7.06/1.67 |
% 7.06/1.67 | ALPHA: (subset_of_empty_set_is_empty_set) implies:
% 7.06/1.67 | (1) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set))
% 7.06/1.68 |
% 7.06/1.68 | ALPHA: (prove_th51) implies:
% 7.06/1.68 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v0 = empty_set) &
% 7.06/1.68 | intersection(v1, v2) = empty_set & $i(v2) & $i(v1) & $i(v0) &
% 7.06/1.68 | subset(v0, v2) & subset(v0, v1))
% 7.06/1.68 |
% 7.06/1.68 | DELTA: instantiating (2) with fresh symbols all_16_0, all_16_1, all_16_2
% 7.06/1.68 | gives:
% 7.06/1.68 | (3) ~ (all_16_2 = empty_set) & intersection(all_16_1, all_16_0) =
% 7.06/1.68 | empty_set & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) &
% 7.06/1.68 | subset(all_16_2, all_16_0) & subset(all_16_2, all_16_1)
% 7.06/1.68 |
% 7.06/1.68 | ALPHA: (3) implies:
% 7.06/1.68 | (4) ~ (all_16_2 = empty_set)
% 7.06/1.68 | (5) subset(all_16_2, all_16_1)
% 7.06/1.68 | (6) subset(all_16_2, all_16_0)
% 7.06/1.68 | (7) $i(all_16_2)
% 7.06/1.68 | (8) $i(all_16_1)
% 7.06/1.68 | (9) $i(all_16_0)
% 7.06/1.68 | (10) intersection(all_16_1, all_16_0) = empty_set
% 7.06/1.68 |
% 7.06/1.68 | GROUND_INST: instantiating (intersection_of_subsets) with all_16_2, all_16_1,
% 7.06/1.68 | all_16_0, empty_set, simplifying with (5), (6), (7), (8), (9),
% 7.06/1.68 | (10) gives:
% 7.06/1.68 | (11) subset(all_16_2, empty_set)
% 7.06/1.68 |
% 7.06/1.68 | GROUND_INST: instantiating (1) with all_16_2, simplifying with (7), (11)
% 7.06/1.68 | gives:
% 7.06/1.68 | (12) all_16_2 = empty_set
% 7.06/1.68 |
% 7.06/1.68 | REDUCE: (4), (12) imply:
% 7.06/1.69 | (13) $false
% 7.06/1.69 |
% 7.06/1.69 | CLOSE: (13) is inconsistent.
% 7.06/1.69 |
% 7.06/1.69 End of proof
% 7.06/1.69 % SZS output end Proof for theBenchmark
% 7.06/1.69
% 7.06/1.69 1082ms
%------------------------------------------------------------------------------