TSTP Solution File: SET596+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET596+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 : n003.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 15:25:29 EDT 2023
% Result : Theorem 5.28s 1.45s
% Output : Proof 7.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET596+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.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 13:36:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 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 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 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 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 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 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 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 ...
% 2.35/1.02 Prover 2: Preprocessing ...
% 2.35/1.02 Prover 5: Preprocessing ...
% 2.35/1.02 Prover 0: Preprocessing ...
% 2.35/1.02 Prover 6: Preprocessing ...
% 2.35/1.02 Prover 3: Preprocessing ...
% 3.74/1.24 Prover 3: Warning: ignoring some quantifiers
% 3.74/1.25 Prover 4: Warning: ignoring some quantifiers
% 3.74/1.25 Prover 1: Warning: ignoring some quantifiers
% 4.20/1.26 Prover 4: Constructing countermodel ...
% 4.20/1.26 Prover 3: Constructing countermodel ...
% 4.20/1.26 Prover 1: Constructing countermodel ...
% 4.20/1.27 Prover 5: Proving ...
% 4.20/1.27 Prover 6: Proving ...
% 4.20/1.27 Prover 2: Proving ...
% 4.20/1.27 Prover 0: Proving ...
% 5.28/1.45 Prover 5: proved (820ms)
% 5.28/1.45 Prover 2: proved (823ms)
% 5.28/1.45
% 5.28/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.28/1.45
% 5.28/1.46
% 5.28/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.28/1.46
% 5.28/1.46 Prover 6: stopped
% 5.28/1.46 Prover 0: stopped
% 5.28/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.28/1.47 Prover 3: stopped
% 5.28/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.28/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.28/1.49 Prover 7: Preprocessing ...
% 5.28/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.28/1.49 Prover 10: Preprocessing ...
% 5.28/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.28/1.49 Prover 8: Preprocessing ...
% 5.28/1.49 Prover 11: Preprocessing ...
% 5.28/1.50 Prover 1: gave up
% 5.28/1.50 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.28/1.51 Prover 4: gave up
% 5.28/1.51 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.28/1.51 Prover 13: Preprocessing ...
% 5.96/1.53 Prover 10: Warning: ignoring some quantifiers
% 5.96/1.54 Prover 16: Preprocessing ...
% 5.96/1.54 Prover 10: Constructing countermodel ...
% 5.96/1.55 Prover 19: Preprocessing ...
% 5.96/1.55 Prover 7: Warning: ignoring some quantifiers
% 5.96/1.56 Prover 7: Constructing countermodel ...
% 6.53/1.60 Prover 13: Warning: ignoring some quantifiers
% 6.53/1.60 Prover 13: Constructing countermodel ...
% 6.53/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.53/1.62 Prover 10: Found proof (size 10)
% 6.53/1.62 Prover 10: proved (154ms)
% 6.53/1.62 Prover 13: stopped
% 6.53/1.62 Prover 7: stopped
% 6.53/1.62 Prover 16: Warning: ignoring some quantifiers
% 6.53/1.63 Prover 8: Constructing countermodel ...
% 6.53/1.63 Prover 16: Constructing countermodel ...
% 6.53/1.64 Prover 16: stopped
% 6.53/1.64 Prover 8: stopped
% 6.53/1.65 Prover 11: Warning: ignoring some quantifiers
% 6.53/1.66 Prover 11: Constructing countermodel ...
% 6.53/1.66 Prover 11: stopped
% 7.08/1.68 Prover 19: Warning: ignoring some quantifiers
% 7.08/1.69 Prover 19: Constructing countermodel ...
% 7.08/1.69 Prover 19: stopped
% 7.08/1.69
% 7.08/1.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.08/1.69
% 7.08/1.69 % SZS output start Proof for theBenchmark
% 7.08/1.70 Assumptions after simplification:
% 7.08/1.70 ---------------------------------
% 7.08/1.70
% 7.08/1.70 (commutativity_of_intersection)
% 7.32/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~
% 7.32/1.72 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 7.32/1.72
% 7.32/1.72 (intersection_of_subset)
% 7.32/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 7.32/1.73 (intersection(v1, v2) = v4) | ~ (intersection(v0, v2) = v3) | ~ $i(v2) |
% 7.32/1.73 ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | subset(v3, v4))
% 7.32/1.73
% 7.32/1.73 (prove_th55)
% 7.32/1.73 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 7.32/1.73 (v3 = empty_set) & intersection(v1, v2) = empty_set & intersection(v0, v2) =
% 7.32/1.73 v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & subset(v0, v1))
% 7.32/1.73
% 7.32/1.73 (subset_of_empty_set_is_empty_set)
% 7.32/1.73 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0,
% 7.32/1.73 empty_set))
% 7.32/1.73
% 7.32/1.73 Further assumptions not needed in the proof:
% 7.32/1.73 --------------------------------------------
% 7.32/1.73 empty_defn, empty_set_defn, equal_defn, equal_member_defn, intersection_defn,
% 7.32/1.73 reflexivity_of_subset, subset_defn
% 7.32/1.73
% 7.32/1.73 Those formulas are unsatisfiable:
% 7.32/1.73 ---------------------------------
% 7.32/1.73
% 7.32/1.73 Begin of proof
% 7.32/1.73 |
% 7.32/1.73 | ALPHA: (subset_of_empty_set_is_empty_set) implies:
% 7.32/1.73 | (1) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ subset(v0, empty_set))
% 7.32/1.73 |
% 7.32/1.73 | ALPHA: (prove_th55) implies:
% 7.32/1.73 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 7.32/1.73 | empty_set) & intersection(v1, v2) = empty_set & intersection(v0,
% 7.32/1.73 | v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & subset(v0, v1))
% 7.32/1.73 |
% 7.32/1.73 | DELTA: instantiating (2) with fresh symbols all_16_0, all_16_1, all_16_2,
% 7.32/1.73 | all_16_3 gives:
% 7.32/1.74 | (3) ~ (all_16_0 = empty_set) & intersection(all_16_2, all_16_1) =
% 7.32/1.74 | empty_set & intersection(all_16_3, all_16_1) = all_16_0 & $i(all_16_0)
% 7.32/1.74 | & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & subset(all_16_3,
% 7.32/1.74 | all_16_2)
% 7.32/1.74 |
% 7.32/1.74 | ALPHA: (3) implies:
% 7.32/1.74 | (4) ~ (all_16_0 = empty_set)
% 7.32/1.74 | (5) subset(all_16_3, all_16_2)
% 7.32/1.74 | (6) $i(all_16_3)
% 7.32/1.74 | (7) $i(all_16_2)
% 7.32/1.74 | (8) $i(all_16_1)
% 7.32/1.74 | (9) intersection(all_16_3, all_16_1) = all_16_0
% 7.32/1.74 | (10) intersection(all_16_2, all_16_1) = empty_set
% 7.32/1.74 |
% 7.32/1.74 | GROUND_INST: instantiating (commutativity_of_intersection) with all_16_3,
% 7.32/1.74 | all_16_1, all_16_0, simplifying with (6), (8), (9) gives:
% 7.32/1.74 | (11) intersection(all_16_1, all_16_3) = all_16_0 & $i(all_16_0)
% 7.32/1.74 |
% 7.32/1.74 | ALPHA: (11) implies:
% 7.32/1.74 | (12) $i(all_16_0)
% 7.32/1.74 |
% 7.32/1.74 | GROUND_INST: instantiating (intersection_of_subset) with all_16_3, all_16_2,
% 7.32/1.74 | all_16_1, all_16_0, empty_set, simplifying with (5), (6), (7),
% 7.32/1.74 | (8), (9), (10) gives:
% 7.32/1.74 | (13) subset(all_16_0, empty_set)
% 7.32/1.74 |
% 7.32/1.74 | GROUND_INST: instantiating (1) with all_16_0, simplifying with (12), (13)
% 7.32/1.74 | gives:
% 7.32/1.74 | (14) all_16_0 = empty_set
% 7.32/1.74 |
% 7.32/1.74 | REDUCE: (4), (14) imply:
% 7.32/1.74 | (15) $false
% 7.32/1.74 |
% 7.32/1.74 | CLOSE: (15) is inconsistent.
% 7.32/1.74 |
% 7.32/1.74 End of proof
% 7.32/1.74 % SZS output end Proof for theBenchmark
% 7.32/1.74
% 7.32/1.74 1136ms
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