TSTP Solution File: SEV421_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEV421_1 : TPTP v8.1.2. Released v5.0.0.
% 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 19:36:51 EDT 2023
% Result : Theorem 6.63s 1.62s
% Output : Proof 7.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV421_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n020.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 : Thu Aug 24 03:37:45 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.05 Prover 1: Preprocessing ...
% 2.75/1.05 Prover 4: Preprocessing ...
% 2.75/1.09 Prover 3: Preprocessing ...
% 2.75/1.09 Prover 6: Preprocessing ...
% 2.75/1.09 Prover 5: Preprocessing ...
% 2.75/1.09 Prover 2: Preprocessing ...
% 2.75/1.09 Prover 0: Preprocessing ...
% 5.16/1.46 Prover 3: Warning: ignoring some quantifiers
% 5.77/1.47 Prover 1: Warning: ignoring some quantifiers
% 5.77/1.49 Prover 3: Constructing countermodel ...
% 5.77/1.49 Prover 1: Constructing countermodel ...
% 5.77/1.50 Prover 6: Proving ...
% 5.77/1.50 Prover 4: Warning: ignoring some quantifiers
% 5.77/1.51 Prover 0: Proving ...
% 5.77/1.52 Prover 5: Proving ...
% 5.77/1.52 Prover 4: Constructing countermodel ...
% 5.77/1.53 Prover 2: Proving ...
% 6.63/1.61 Prover 3: proved (996ms)
% 6.63/1.62
% 6.63/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/1.62
% 6.63/1.62 Prover 0: stopped
% 6.63/1.62 Prover 2: stopped
% 6.63/1.62 Prover 5: stopped
% 6.63/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.63/1.63 Prover 6: proved (997ms)
% 6.63/1.63
% 6.63/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/1.63
% 6.63/1.63 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.63/1.63 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.00/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.00/1.63 Prover 1: Found proof (size 15)
% 7.00/1.63 Prover 1: proved (1016ms)
% 7.00/1.64 Prover 4: stopped
% 7.00/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.13/1.67 Prover 8: Preprocessing ...
% 7.13/1.67 Prover 11: Preprocessing ...
% 7.13/1.67 Prover 13: Preprocessing ...
% 7.13/1.68 Prover 7: Preprocessing ...
% 7.13/1.68 Prover 10: Preprocessing ...
% 7.13/1.71 Prover 10: stopped
% 7.64/1.72 Prover 7: stopped
% 7.64/1.72 Prover 11: stopped
% 7.64/1.73 Prover 13: stopped
% 7.89/1.77 Prover 8: Warning: ignoring some quantifiers
% 7.89/1.78 Prover 8: Constructing countermodel ...
% 7.89/1.78 Prover 8: stopped
% 7.89/1.78
% 7.89/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.89/1.78
% 7.89/1.79 % SZS output start Proof for theBenchmark
% 7.89/1.79 Assumptions after simplification:
% 7.89/1.79 ---------------------------------
% 7.89/1.79
% 7.89/1.79 (cardinality_empty_set)
% 7.89/1.81 set(empty_set) & ! [v0: set] : (v0 = empty_set | ~ (cardinality(v0) = 0) |
% 7.89/1.81 ~ set(v0)) & ! [v0: int] : (v0 = 0 | ~ (cardinality(empty_set) = v0))
% 7.89/1.81
% 7.89/1.81 (vc1)
% 7.89/1.82 set(empty_set) & ? [v0: element] : ? [v1: set] : ? [v2: int] : ? [v3: int]
% 7.89/1.82 : ( ~ (v3 = 0) & cardinality(v1) = v2 & member(v0, v1) = v3 & element(v0) &
% 7.89/1.82 set(v1) & ((v2 = 0 & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = 0))))
% 7.89/1.82
% 7.89/1.82 Further assumptions not needed in the proof:
% 7.89/1.82 --------------------------------------------
% 7.89/1.82 cardinality_intersection_1, cardinality_intersection_2,
% 7.89/1.82 cardinality_intersection_3, cardinality_union, complement, difference,
% 7.89/1.82 empty_set, intersection, singleton, subset, union
% 7.89/1.82
% 7.89/1.82 Those formulas are unsatisfiable:
% 7.89/1.82 ---------------------------------
% 7.89/1.82
% 7.89/1.82 Begin of proof
% 7.89/1.82 |
% 7.89/1.82 | ALPHA: (cardinality_empty_set) implies:
% 7.89/1.82 | (1) ! [v0: int] : (v0 = 0 | ~ (cardinality(empty_set) = v0))
% 7.89/1.82 | (2) ! [v0: set] : (v0 = empty_set | ~ (cardinality(v0) = 0) | ~ set(v0))
% 7.89/1.82 |
% 7.89/1.82 | ALPHA: (vc1) implies:
% 7.89/1.82 | (3) ? [v0: element] : ? [v1: set] : ? [v2: int] : ? [v3: int] : ( ~ (v3
% 7.89/1.82 | = 0) & cardinality(v1) = v2 & member(v0, v1) = v3 & element(v0) &
% 7.89/1.82 | set(v1) & ((v2 = 0 & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2
% 7.89/1.82 | = 0))))
% 7.89/1.82 |
% 7.89/1.82 | DELTA: instantiating (3) with fresh symbols all_21_0, all_21_1, all_21_2,
% 7.89/1.82 | all_21_3 gives:
% 7.89/1.82 | (4) ~ (all_21_0 = 0) & cardinality(all_21_2) = all_21_1 & member(all_21_3,
% 7.89/1.82 | all_21_2) = all_21_0 & element(all_21_3) & set(all_21_2) & ((all_21_1
% 7.89/1.82 | = 0 & ~ (all_21_2 = empty_set)) | (all_21_2 = empty_set & ~
% 7.89/1.82 | (all_21_1 = 0)))
% 7.89/1.82 |
% 7.89/1.82 | ALPHA: (4) implies:
% 7.89/1.82 | (5) set(all_21_2)
% 7.89/1.82 | (6) cardinality(all_21_2) = all_21_1
% 7.89/1.83 | (7) (all_21_1 = 0 & ~ (all_21_2 = empty_set)) | (all_21_2 = empty_set & ~
% 7.89/1.83 | (all_21_1 = 0))
% 7.89/1.83 |
% 7.89/1.83 | BETA: splitting (7) gives:
% 7.89/1.83 |
% 7.89/1.83 | Case 1:
% 7.89/1.83 | |
% 7.89/1.83 | | (8) all_21_1 = 0 & ~ (all_21_2 = empty_set)
% 7.89/1.83 | |
% 7.89/1.83 | | ALPHA: (8) implies:
% 7.89/1.83 | | (9) all_21_1 = 0
% 7.89/1.83 | | (10) ~ (all_21_2 = empty_set)
% 7.89/1.83 | |
% 7.89/1.83 | | REDUCE: (6), (9) imply:
% 7.89/1.83 | | (11) cardinality(all_21_2) = 0
% 7.89/1.83 | |
% 7.89/1.83 | | GROUND_INST: instantiating (2) with all_21_2, simplifying with (5), (11)
% 7.89/1.83 | | gives:
% 7.89/1.83 | | (12) all_21_2 = empty_set
% 7.89/1.83 | |
% 7.89/1.83 | | REDUCE: (10), (12) imply:
% 7.89/1.83 | | (13) $false
% 7.89/1.83 | |
% 7.89/1.83 | | CLOSE: (13) is inconsistent.
% 7.89/1.83 | |
% 7.89/1.83 | Case 2:
% 7.89/1.83 | |
% 7.89/1.83 | | (14) all_21_2 = empty_set & ~ (all_21_1 = 0)
% 7.89/1.83 | |
% 7.89/1.83 | | ALPHA: (14) implies:
% 7.89/1.83 | | (15) all_21_2 = empty_set
% 7.89/1.83 | | (16) ~ (all_21_1 = 0)
% 7.89/1.83 | |
% 7.89/1.83 | | REDUCE: (6), (15) imply:
% 7.89/1.83 | | (17) cardinality(empty_set) = all_21_1
% 7.89/1.83 | |
% 7.89/1.83 | | GROUND_INST: instantiating (1) with all_21_1, simplifying with (17) gives:
% 7.89/1.83 | | (18) all_21_1 = 0
% 7.89/1.83 | |
% 7.89/1.83 | | REDUCE: (16), (18) imply:
% 7.89/1.83 | | (19) $false
% 7.89/1.83 | |
% 7.89/1.83 | | CLOSE: (19) is inconsistent.
% 7.89/1.83 | |
% 7.89/1.83 | End of split
% 7.89/1.83 |
% 7.89/1.83 End of proof
% 7.89/1.83 % SZS output end Proof for theBenchmark
% 7.89/1.83
% 7.89/1.83 1233ms
%------------------------------------------------------------------------------