TSTP Solution File: SET590+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET590+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 : n008.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 3.69s 1.25s
% Output : Proof 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET590+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 : n008.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 09:39:47 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.65/0.96 Prover 4: Preprocessing ...
% 1.65/0.96 Prover 1: Preprocessing ...
% 2.05/1.00 Prover 2: Preprocessing ...
% 2.05/1.00 Prover 5: Preprocessing ...
% 2.05/1.00 Prover 6: Preprocessing ...
% 2.05/1.00 Prover 3: Preprocessing ...
% 2.05/1.00 Prover 0: Preprocessing ...
% 3.23/1.14 Prover 5: Proving ...
% 3.23/1.14 Prover 6: Proving ...
% 3.23/1.14 Prover 2: Proving ...
% 3.23/1.15 Prover 1: Constructing countermodel ...
% 3.23/1.15 Prover 4: Constructing countermodel ...
% 3.23/1.15 Prover 3: Constructing countermodel ...
% 3.23/1.15 Prover 0: Proving ...
% 3.69/1.24 Prover 3: proved (608ms)
% 3.69/1.25
% 3.69/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/1.25
% 3.69/1.25 Prover 5: stopped
% 3.69/1.25 Prover 2: stopped
% 3.69/1.25 Prover 6: stopped
% 3.69/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.69/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.69/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.69/1.25 Prover 0: stopped
% 3.69/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.69/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.08/1.27 Prover 10: Preprocessing ...
% 4.08/1.27 Prover 11: Preprocessing ...
% 4.08/1.27 Prover 13: Preprocessing ...
% 4.08/1.27 Prover 7: Preprocessing ...
% 4.08/1.28 Prover 8: Preprocessing ...
% 4.08/1.29 Prover 10: Warning: ignoring some quantifiers
% 4.08/1.30 Prover 10: Constructing countermodel ...
% 4.08/1.30 Prover 4: Found proof (size 17)
% 4.08/1.30 Prover 4: proved (651ms)
% 4.08/1.30 Prover 7: Warning: ignoring some quantifiers
% 4.08/1.30 Prover 1: stopped
% 4.08/1.31 Prover 7: Constructing countermodel ...
% 4.08/1.31 Prover 10: stopped
% 4.08/1.31 Prover 7: stopped
% 4.08/1.32 Prover 13: Warning: ignoring some quantifiers
% 4.08/1.32 Prover 13: Constructing countermodel ...
% 4.08/1.33 Prover 13: stopped
% 4.08/1.33 Prover 8: Warning: ignoring some quantifiers
% 4.08/1.34 Prover 11: Constructing countermodel ...
% 4.08/1.34 Prover 8: Constructing countermodel ...
% 4.08/1.34 Prover 11: stopped
% 4.08/1.34 Prover 8: stopped
% 4.08/1.34
% 4.08/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/1.34
% 4.08/1.35 % SZS output start Proof for theBenchmark
% 4.08/1.35 Assumptions after simplification:
% 4.08/1.35 ---------------------------------
% 4.08/1.35
% 4.08/1.35 (difference_defn)
% 4.71/1.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 4.71/1.38 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 4.71/1.38 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 4.71/1.38 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 4.71/1.38 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2,
% 4.71/1.38 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 4.71/1.39 0) & member(v2, v1) = v4 & member(v2, v0) = 0))
% 4.71/1.39
% 4.71/1.39 (prove_th49)
% 4.71/1.39 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 4.71/1.39 subset(v2, v0) = v3 & difference(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0))
% 4.71/1.39
% 4.71/1.39 (subset_defn)
% 4.71/1.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 4.71/1.39 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 4.71/1.39 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 4.71/1.39 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 4.71/1.39 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 4.71/1.39 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 4.71/1.39 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 4.71/1.39 ~ $i(v0) | member(v2, v1) = 0)
% 4.71/1.39
% 4.71/1.39 (function-axioms)
% 4.71/1.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 4.71/1.40 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 4.71/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 4.71/1.40 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0:
% 4.71/1.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 4.71/1.40 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 4.71/1.40
% 4.71/1.40 Further assumptions not needed in the proof:
% 4.71/1.40 --------------------------------------------
% 4.71/1.40 reflexivity_of_subset
% 4.71/1.40
% 4.71/1.40 Those formulas are unsatisfiable:
% 4.71/1.40 ---------------------------------
% 4.71/1.40
% 4.71/1.40 Begin of proof
% 4.71/1.40 |
% 4.71/1.40 | ALPHA: (difference_defn) implies:
% 4.71/1.40 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 4.71/1.40 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~
% 4.71/1.40 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) =
% 4.71/1.40 | v4 & member(v2, v0) = 0))
% 4.71/1.40 |
% 4.71/1.40 | ALPHA: (subset_defn) implies:
% 4.71/1.40 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 4.71/1.40 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 4.71/1.40 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 4.71/1.40 |
% 4.71/1.40 | ALPHA: (function-axioms) implies:
% 4.71/1.40 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 4.71/1.40 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 4.71/1.40 | = v0))
% 4.71/1.40 |
% 4.71/1.40 | DELTA: instantiating (prove_th49) with fresh symbols all_6_0, all_6_1,
% 4.71/1.40 | all_6_2, all_6_3 gives:
% 4.71/1.40 | (4) ~ (all_6_0 = 0) & subset(all_6_1, all_6_3) = all_6_0 &
% 4.71/1.40 | difference(all_6_3, all_6_2) = all_6_1 & $i(all_6_1) & $i(all_6_2) &
% 4.71/1.40 | $i(all_6_3)
% 4.71/1.40 |
% 4.71/1.40 | ALPHA: (4) implies:
% 4.71/1.41 | (5) ~ (all_6_0 = 0)
% 4.71/1.41 | (6) $i(all_6_3)
% 4.71/1.41 | (7) $i(all_6_2)
% 4.71/1.41 | (8) $i(all_6_1)
% 4.71/1.41 | (9) difference(all_6_3, all_6_2) = all_6_1
% 4.71/1.41 | (10) subset(all_6_1, all_6_3) = all_6_0
% 4.71/1.41 |
% 4.71/1.41 | GROUND_INST: instantiating (2) with all_6_1, all_6_3, all_6_0, simplifying
% 4.71/1.41 | with (6), (8), (10) gives:
% 4.71/1.41 | (11) all_6_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 4.71/1.41 | all_6_1) = 0 & member(v0, all_6_3) = v1 & $i(v0))
% 4.71/1.41 |
% 4.71/1.41 | BETA: splitting (11) gives:
% 4.71/1.41 |
% 4.71/1.41 | Case 1:
% 4.71/1.41 | |
% 4.71/1.41 | | (12) all_6_0 = 0
% 4.71/1.41 | |
% 4.71/1.41 | | REDUCE: (5), (12) imply:
% 4.71/1.41 | | (13) $false
% 4.71/1.41 | |
% 4.71/1.41 | | CLOSE: (13) is inconsistent.
% 4.71/1.41 | |
% 4.71/1.41 | Case 2:
% 4.71/1.41 | |
% 4.71/1.41 | | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_1) = 0
% 4.71/1.41 | | & member(v0, all_6_3) = v1 & $i(v0))
% 4.71/1.41 | |
% 4.71/1.41 | | DELTA: instantiating (14) with fresh symbols all_15_0, all_15_1 gives:
% 4.71/1.41 | | (15) ~ (all_15_0 = 0) & member(all_15_1, all_6_1) = 0 & member(all_15_1,
% 4.71/1.41 | | all_6_3) = all_15_0 & $i(all_15_1)
% 4.71/1.41 | |
% 4.71/1.41 | | ALPHA: (15) implies:
% 4.71/1.41 | | (16) ~ (all_15_0 = 0)
% 4.71/1.41 | | (17) $i(all_15_1)
% 4.71/1.41 | | (18) member(all_15_1, all_6_3) = all_15_0
% 4.71/1.41 | | (19) member(all_15_1, all_6_1) = 0
% 4.71/1.41 | |
% 4.71/1.42 | | GROUND_INST: instantiating (1) with all_6_3, all_6_2, all_15_1, all_6_1,
% 4.71/1.42 | | simplifying with (6), (7), (9), (17), (19) gives:
% 4.71/1.42 | | (20) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_1, all_6_2) = v0 &
% 4.71/1.42 | | member(all_15_1, all_6_3) = 0)
% 4.71/1.42 | |
% 4.71/1.42 | | DELTA: instantiating (20) with fresh symbol all_22_0 gives:
% 4.71/1.42 | | (21) ~ (all_22_0 = 0) & member(all_15_1, all_6_2) = all_22_0 &
% 4.71/1.42 | | member(all_15_1, all_6_3) = 0
% 4.71/1.42 | |
% 4.71/1.42 | | ALPHA: (21) implies:
% 4.71/1.42 | | (22) member(all_15_1, all_6_3) = 0
% 4.71/1.42 | |
% 4.71/1.42 | | GROUND_INST: instantiating (3) with all_15_0, 0, all_6_3, all_15_1,
% 4.71/1.42 | | simplifying with (18), (22) gives:
% 4.71/1.42 | | (23) all_15_0 = 0
% 4.71/1.42 | |
% 4.71/1.42 | | REDUCE: (16), (23) imply:
% 4.71/1.42 | | (24) $false
% 4.71/1.42 | |
% 4.71/1.42 | | CLOSE: (24) is inconsistent.
% 4.71/1.42 | |
% 4.71/1.42 | End of split
% 4.71/1.42 |
% 4.71/1.42 End of proof
% 4.71/1.42 % SZS output end Proof for theBenchmark
% 4.71/1.42
% 4.71/1.42 809ms
%------------------------------------------------------------------------------