TSTP Solution File: SET813+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 15:26:33 EDT 2023
% Result : Theorem 9.93s 2.22s
% Output : Proof 12.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:58:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.83/1.13 Prover 1: Preprocessing ...
% 2.83/1.13 Prover 4: Preprocessing ...
% 2.83/1.17 Prover 2: Preprocessing ...
% 2.83/1.17 Prover 3: Preprocessing ...
% 2.83/1.17 Prover 5: Preprocessing ...
% 2.83/1.17 Prover 6: Preprocessing ...
% 2.83/1.17 Prover 0: Preprocessing ...
% 7.19/1.73 Prover 6: Proving ...
% 7.19/1.74 Prover 5: Proving ...
% 7.19/1.74 Prover 1: Constructing countermodel ...
% 7.19/1.75 Prover 3: Constructing countermodel ...
% 7.19/1.75 Prover 2: Proving ...
% 7.72/1.85 Prover 3: gave up
% 7.72/1.86 Prover 6: gave up
% 7.72/1.86 Prover 1: gave up
% 8.39/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.39/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.39/1.87 Prover 4: Constructing countermodel ...
% 8.39/1.87 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.83/1.94 Prover 7: Preprocessing ...
% 8.83/1.94 Prover 0: Proving ...
% 8.83/1.94 Prover 8: Preprocessing ...
% 8.83/1.95 Prover 9: Preprocessing ...
% 9.93/2.09 Prover 7: Warning: ignoring some quantifiers
% 9.93/2.13 Prover 7: Constructing countermodel ...
% 9.93/2.13 Prover 8: Warning: ignoring some quantifiers
% 9.93/2.16 Prover 8: Constructing countermodel ...
% 9.93/2.21 Prover 0: proved (1586ms)
% 9.93/2.21
% 9.93/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.93/2.22
% 9.93/2.23 Prover 5: stopped
% 9.93/2.24 Prover 2: stopped
% 9.93/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.93/2.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.93/2.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.93/2.27 Prover 10: Preprocessing ...
% 11.22/2.30 Prover 13: Preprocessing ...
% 11.22/2.31 Prover 11: Preprocessing ...
% 11.48/2.32 Prover 8: gave up
% 11.48/2.33 Prover 10: Warning: ignoring some quantifiers
% 11.48/2.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.69/2.35 Prover 10: Constructing countermodel ...
% 11.69/2.37 Prover 9: Constructing countermodel ...
% 11.69/2.37 Prover 16: Preprocessing ...
% 11.69/2.38 Prover 4: Found proof (size 24)
% 11.69/2.38 Prover 4: proved (1740ms)
% 11.69/2.38 Prover 9: stopped
% 11.69/2.38 Prover 7: stopped
% 11.69/2.38 Prover 10: stopped
% 11.69/2.38 Prover 13: stopped
% 11.69/2.38 Prover 11: stopped
% 11.69/2.39 Prover 16: stopped
% 11.69/2.39
% 11.69/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.69/2.39
% 11.69/2.39 % SZS output start Proof for theBenchmark
% 11.69/2.40 Assumptions after simplification:
% 11.69/2.40 ---------------------------------
% 11.69/2.40
% 11.69/2.40 (singleton)
% 11.69/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) |
% 11.69/2.42 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.69/2.42 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~
% 11.69/2.42 $i(v1) | ~ $i(v0))
% 11.69/2.42
% 11.69/2.42 (successor)
% 12.19/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.19/2.43 | ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) =
% 12.19/2.43 v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 12.19/2.43 suc(v0) = v5 & member(v1, v5) = v6 & $i(v5))) & ! [v0: $i] : ! [v1: $i]
% 12.19/2.43 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (suc(v0) = v2) | ~ (member(v1,
% 12.19/2.43 v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 12.19/2.43 int] : ( ~ (v6 = 0) & singleton(v0) = v4 & union(v0, v4) = v5 & member(v1,
% 12.19/2.43 v5) = v6 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.19/2.43 ! [v3: $i] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~
% 12.19/2.43 (member(v1, v3) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (suc(v0) = v4 &
% 12.19/2.43 member(v1, v4) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.19/2.43 ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 12.19/2.43 $i] : ? [v4: $i] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1,
% 12.19/2.43 v4) = 0 & $i(v4) & $i(v3)))
% 12.19/2.43
% 12.19/2.43 (thV12)
% 12.19/2.43 $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & suc(v0) =
% 12.19/2.43 v1 & member(v0, v1) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0))
% 12.19/2.43
% 12.19/2.43 (union)
% 12.19/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 12.19/2.44 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1)
% 12.19/2.44 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) &
% 12.19/2.44 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 12.19/2.44 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0)
% 12.19/2.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 12.19/2.44 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 12.19/2.44
% 12.19/2.44 Further assumptions not needed in the proof:
% 12.19/2.44 --------------------------------------------
% 12.19/2.44 difference, empty_set, equal_set, initial_segment, intersection, least,
% 12.19/2.44 ordinal_number, power_set, product, rel_member, set_member, strict_order,
% 12.19/2.44 strict_well_order, subset, sum, unordered_pair
% 12.19/2.44
% 12.19/2.44 Those formulas are unsatisfiable:
% 12.19/2.44 ---------------------------------
% 12.19/2.44
% 12.19/2.44 Begin of proof
% 12.19/2.44 |
% 12.19/2.44 | ALPHA: (union) implies:
% 12.19/2.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.19/2.44 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~
% 12.19/2.44 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~
% 12.19/2.44 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) =
% 12.19/2.44 | v5))
% 12.19/2.44 |
% 12.19/2.44 | ALPHA: (singleton) implies:
% 12.19/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0)
% 12.19/2.45 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0))
% 12.19/2.45 |
% 12.19/2.45 | ALPHA: (successor) implies:
% 12.19/2.45 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.19/2.45 | (suc(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) |
% 12.19/2.45 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 12.19/2.45 | singleton(v0) = v4 & union(v0, v4) = v5 & member(v1, v5) = v6 &
% 12.19/2.45 | $i(v5) & $i(v4)))
% 12.19/2.45 |
% 12.19/2.45 | ALPHA: (thV12) implies:
% 12.19/2.45 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & suc(v0) = v1
% 12.19/2.45 | & member(v0, v1) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0))
% 12.19/2.45 |
% 12.19/2.45 | DELTA: instantiating (4) with fresh symbols all_23_0, all_23_1, all_23_2
% 12.19/2.45 | gives:
% 12.19/2.45 | (5) ~ (all_23_0 = 0) & suc(all_23_2) = all_23_1 & member(all_23_2,
% 12.19/2.45 | all_23_1) = all_23_0 & member(all_23_2, on) = 0 & $i(all_23_1) &
% 12.19/2.45 | $i(all_23_2)
% 12.19/2.45 |
% 12.19/2.45 | ALPHA: (5) implies:
% 12.19/2.45 | (6) ~ (all_23_0 = 0)
% 12.19/2.45 | (7) $i(all_23_2)
% 12.19/2.45 | (8) member(all_23_2, all_23_1) = all_23_0
% 12.19/2.45 | (9) suc(all_23_2) = all_23_1
% 12.19/2.45 |
% 12.19/2.45 | GROUND_INST: instantiating (3) with all_23_2, all_23_2, all_23_1, all_23_0,
% 12.19/2.45 | simplifying with (7), (8), (9) gives:
% 12.19/2.46 | (10) all_23_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 12.19/2.46 | & singleton(all_23_2) = v0 & union(all_23_2, v0) = v1 &
% 12.19/2.46 | member(all_23_2, v1) = v2 & $i(v1) & $i(v0))
% 12.19/2.46 |
% 12.19/2.46 | BETA: splitting (10) gives:
% 12.19/2.46 |
% 12.19/2.46 | Case 1:
% 12.19/2.46 | |
% 12.19/2.46 | | (11) all_23_0 = 0
% 12.19/2.46 | |
% 12.19/2.46 | | REDUCE: (6), (11) imply:
% 12.19/2.46 | | (12) $false
% 12.19/2.46 | |
% 12.19/2.46 | | CLOSE: (12) is inconsistent.
% 12.19/2.46 | |
% 12.19/2.46 | Case 2:
% 12.19/2.46 | |
% 12.19/2.46 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 12.19/2.46 | | singleton(all_23_2) = v0 & union(all_23_2, v0) = v1 &
% 12.19/2.46 | | member(all_23_2, v1) = v2 & $i(v1) & $i(v0))
% 12.19/2.46 | |
% 12.19/2.46 | | DELTA: instantiating (13) with fresh symbols all_40_0, all_40_1, all_40_2
% 12.19/2.46 | | gives:
% 12.19/2.46 | | (14) ~ (all_40_0 = 0) & singleton(all_23_2) = all_40_2 & union(all_23_2,
% 12.19/2.46 | | all_40_2) = all_40_1 & member(all_23_2, all_40_1) = all_40_0 &
% 12.19/2.46 | | $i(all_40_1) & $i(all_40_2)
% 12.19/2.46 | |
% 12.19/2.46 | | ALPHA: (14) implies:
% 12.19/2.46 | | (15) ~ (all_40_0 = 0)
% 12.19/2.46 | | (16) $i(all_40_2)
% 12.19/2.46 | | (17) member(all_23_2, all_40_1) = all_40_0
% 12.19/2.46 | | (18) union(all_23_2, all_40_2) = all_40_1
% 12.19/2.46 | | (19) singleton(all_23_2) = all_40_2
% 12.19/2.46 | |
% 12.19/2.46 | | GROUND_INST: instantiating (1) with all_23_2, all_23_2, all_40_2, all_40_1,
% 12.19/2.46 | | all_40_0, simplifying with (7), (16), (17), (18) gives:
% 12.19/2.46 | | (20) all_40_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 12.19/2.46 | | 0) & member(all_23_2, all_40_2) = v1 & member(all_23_2,
% 12.19/2.46 | | all_23_2) = v0)
% 12.19/2.46 | |
% 12.19/2.46 | | BETA: splitting (20) gives:
% 12.19/2.46 | |
% 12.19/2.46 | | Case 1:
% 12.19/2.46 | | |
% 12.19/2.46 | | | (21) all_40_0 = 0
% 12.19/2.46 | | |
% 12.19/2.46 | | | REDUCE: (15), (21) imply:
% 12.19/2.46 | | | (22) $false
% 12.19/2.46 | | |
% 12.19/2.46 | | | CLOSE: (22) is inconsistent.
% 12.19/2.46 | | |
% 12.19/2.46 | | Case 2:
% 12.19/2.46 | | |
% 12.19/2.46 | | | (23) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 12.19/2.46 | | | member(all_23_2, all_40_2) = v1 & member(all_23_2, all_23_2) =
% 12.19/2.46 | | | v0)
% 12.19/2.46 | | |
% 12.19/2.46 | | | DELTA: instantiating (23) with fresh symbols all_65_0, all_65_1 gives:
% 12.19/2.46 | | | (24) ~ (all_65_0 = 0) & ~ (all_65_1 = 0) & member(all_23_2, all_40_2)
% 12.19/2.46 | | | = all_65_0 & member(all_23_2, all_23_2) = all_65_1
% 12.19/2.46 | | |
% 12.19/2.46 | | | ALPHA: (24) implies:
% 12.19/2.47 | | | (25) ~ (all_65_0 = 0)
% 12.19/2.47 | | | (26) member(all_23_2, all_40_2) = all_65_0
% 12.19/2.47 | | |
% 12.19/2.47 | | | GROUND_INST: instantiating (2) with all_23_2, all_40_2, all_65_0,
% 12.19/2.47 | | | simplifying with (7), (19), (26) gives:
% 12.19/2.47 | | | (27) all_65_0 = 0
% 12.19/2.47 | | |
% 12.19/2.47 | | | REDUCE: (25), (27) imply:
% 12.19/2.47 | | | (28) $false
% 12.19/2.47 | | |
% 12.19/2.47 | | | CLOSE: (28) is inconsistent.
% 12.19/2.47 | | |
% 12.19/2.47 | | End of split
% 12.19/2.47 | |
% 12.19/2.47 | End of split
% 12.19/2.47 |
% 12.19/2.47 End of proof
% 12.19/2.47 % SZS output end Proof for theBenchmark
% 12.19/2.47
% 12.19/2.47 1858ms
%------------------------------------------------------------------------------