TSTP Solution File: SET705+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET705+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 15:26:04 EDT 2023
% Result : Theorem 5.02s 1.50s
% Output : Proof 7.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET705+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sat Aug 26 09:40:43 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.54 ________ _____
% 0.15/0.54 ___ __ \_________(_)________________________________
% 0.15/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.15/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.15/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.15/0.54
% 0.15/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.54 (2023-06-19)
% 0.15/0.54
% 0.15/0.54 (c) Philipp Rümmer, 2009-2023
% 0.15/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.54 Amanda Stjerna.
% 0.15/0.54 Free software under BSD-3-Clause.
% 0.15/0.54
% 0.15/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.54
% 0.15/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.15/0.55 Running up to 7 provers in parallel.
% 0.15/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.10/0.92 Prover 1: Preprocessing ...
% 2.10/0.92 Prover 4: Preprocessing ...
% 2.10/0.96 Prover 2: Preprocessing ...
% 2.10/0.96 Prover 3: Preprocessing ...
% 2.10/0.97 Prover 6: Preprocessing ...
% 2.10/0.97 Prover 5: Preprocessing ...
% 2.10/0.97 Prover 0: Preprocessing ...
% 5.02/1.35 Prover 6: Proving ...
% 5.02/1.36 Prover 5: Proving ...
% 5.02/1.36 Prover 1: Constructing countermodel ...
% 5.02/1.37 Prover 3: Constructing countermodel ...
% 5.02/1.38 Prover 2: Proving ...
% 5.02/1.41 Prover 4: Constructing countermodel ...
% 5.02/1.42 Prover 0: Proving ...
% 5.02/1.50 Prover 3: proved (942ms)
% 5.02/1.50
% 5.02/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.02/1.50
% 5.02/1.51 Prover 5: stopped
% 5.02/1.52 Prover 2: stopped
% 5.02/1.52 Prover 0: stopped
% 5.02/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.02/1.52 Prover 6: proved (955ms)
% 5.02/1.52
% 5.02/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.02/1.52
% 6.34/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.34/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.34/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.34/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.34/1.54 Prover 1: Found proof (size 20)
% 6.34/1.55 Prover 1: proved (988ms)
% 6.34/1.55 Prover 4: stopped
% 6.34/1.56 Prover 7: Preprocessing ...
% 6.34/1.56 Prover 11: Preprocessing ...
% 6.34/1.56 Prover 8: Preprocessing ...
% 6.34/1.57 Prover 10: Preprocessing ...
% 6.34/1.58 Prover 13: Preprocessing ...
% 6.34/1.59 Prover 10: stopped
% 6.34/1.60 Prover 7: stopped
% 6.34/1.60 Prover 11: stopped
% 6.34/1.61 Prover 13: stopped
% 7.16/1.66 Prover 8: Warning: ignoring some quantifiers
% 7.16/1.67 Prover 8: Constructing countermodel ...
% 7.16/1.68 Prover 8: stopped
% 7.16/1.68
% 7.16/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.16/1.68
% 7.16/1.68 % SZS output start Proof for theBenchmark
% 7.16/1.69 Assumptions after simplification:
% 7.16/1.69 ---------------------------------
% 7.16/1.69
% 7.16/1.69 (power_set)
% 7.54/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.54/1.73 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 7.54/1.73 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 7.54/1.73 : ! [v2: $i] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1)
% 7.54/1.73 | ~ $i(v0) | subset(v0, v1) = 0)
% 7.54/1.73
% 7.54/1.73 (subset)
% 7.54/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.54/1.74 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.54/1.74 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.54/1.74 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.54/1.74 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.54/1.74
% 7.54/1.74 (thI48)
% 7.54/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & power_set(v0) = v1 &
% 7.54/1.74 member(v0, v1) = v2 & $i(v1) & $i(v0))
% 7.54/1.74
% 7.54/1.74 (function-axioms)
% 7.54/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.54/1.75 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.54/1.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.54/1.75 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.54/1.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.54/1.75 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.54/1.75 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 7.54/1.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.54/1.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 7.54/1.75 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.54/1.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.54/1.75 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.54/1.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.54/1.75 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.54/1.75 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 7.54/1.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 7.54/1.75 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 7.54/1.75 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 7.54/1.75 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 7.54/1.75 (power_set(v2) = v0))
% 7.54/1.75
% 7.54/1.75 Further assumptions not needed in the proof:
% 7.54/1.75 --------------------------------------------
% 7.54/1.75 difference, empty_set, equal_set, intersection, product, singleton, sum, union,
% 7.54/1.75 unordered_pair
% 7.54/1.75
% 7.54/1.75 Those formulas are unsatisfiable:
% 7.54/1.75 ---------------------------------
% 7.54/1.75
% 7.54/1.75 Begin of proof
% 7.54/1.75 |
% 7.54/1.75 | ALPHA: (subset) implies:
% 7.54/1.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.54/1.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.54/1.76 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.54/1.76 |
% 7.54/1.76 | ALPHA: (power_set) implies:
% 7.54/1.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.54/1.76 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~
% 7.54/1.76 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.54/1.76 |
% 7.54/1.76 | ALPHA: (function-axioms) implies:
% 7.54/1.76 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.54/1.76 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.54/1.76 | = v0))
% 7.54/1.76 |
% 7.54/1.76 | DELTA: instantiating (thI48) with fresh symbols all_15_0, all_15_1, all_15_2
% 7.54/1.76 | gives:
% 7.54/1.76 | (4) ~ (all_15_0 = 0) & power_set(all_15_2) = all_15_1 & member(all_15_2,
% 7.54/1.76 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2)
% 7.54/1.76 |
% 7.54/1.76 | ALPHA: (4) implies:
% 7.54/1.76 | (5) ~ (all_15_0 = 0)
% 7.54/1.76 | (6) $i(all_15_2)
% 7.54/1.76 | (7) member(all_15_2, all_15_1) = all_15_0
% 7.54/1.76 | (8) power_set(all_15_2) = all_15_1
% 7.54/1.76 |
% 7.54/1.76 | GROUND_INST: instantiating (2) with all_15_2, all_15_2, all_15_1, all_15_0,
% 7.54/1.76 | simplifying with (6), (7), (8) gives:
% 7.54/1.76 | (9) all_15_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_15_2, all_15_2)
% 7.54/1.76 | = v0)
% 7.54/1.76 |
% 7.54/1.76 | BETA: splitting (9) gives:
% 7.54/1.76 |
% 7.54/1.77 | Case 1:
% 7.54/1.77 | |
% 7.54/1.77 | | (10) all_15_0 = 0
% 7.54/1.77 | |
% 7.54/1.77 | | REDUCE: (5), (10) imply:
% 7.54/1.77 | | (11) $false
% 7.54/1.77 | |
% 7.54/1.77 | | CLOSE: (11) is inconsistent.
% 7.54/1.77 | |
% 7.54/1.77 | Case 2:
% 7.54/1.77 | |
% 7.54/1.77 | | (12) ? [v0: int] : ( ~ (v0 = 0) & subset(all_15_2, all_15_2) = v0)
% 7.54/1.77 | |
% 7.54/1.77 | | DELTA: instantiating (12) with fresh symbol all_24_0 gives:
% 7.54/1.77 | | (13) ~ (all_24_0 = 0) & subset(all_15_2, all_15_2) = all_24_0
% 7.54/1.77 | |
% 7.54/1.77 | | ALPHA: (13) implies:
% 7.54/1.77 | | (14) ~ (all_24_0 = 0)
% 7.54/1.77 | | (15) subset(all_15_2, all_15_2) = all_24_0
% 7.54/1.77 | |
% 7.54/1.77 | | GROUND_INST: instantiating (1) with all_15_2, all_15_2, all_24_0,
% 7.54/1.77 | | simplifying with (6), (15) gives:
% 7.54/1.77 | | (16) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 7.54/1.77 | | member(v0, all_15_2) = v1 & member(v0, all_15_2) = 0 & $i(v0))
% 7.54/1.77 | |
% 7.54/1.77 | | BETA: splitting (16) gives:
% 7.54/1.77 | |
% 7.54/1.77 | | Case 1:
% 7.54/1.77 | | |
% 7.54/1.77 | | | (17) all_24_0 = 0
% 7.54/1.77 | | |
% 7.54/1.77 | | | REDUCE: (14), (17) imply:
% 7.54/1.77 | | | (18) $false
% 7.54/1.77 | | |
% 7.54/1.77 | | | CLOSE: (18) is inconsistent.
% 7.54/1.77 | | |
% 7.54/1.77 | | Case 2:
% 7.54/1.77 | | |
% 7.54/1.77 | | | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) =
% 7.54/1.77 | | | v1 & member(v0, all_15_2) = 0 & $i(v0))
% 7.54/1.77 | | |
% 7.54/1.77 | | | DELTA: instantiating (19) with fresh symbols all_33_0, all_33_1 gives:
% 7.54/1.77 | | | (20) ~ (all_33_0 = 0) & member(all_33_1, all_15_2) = all_33_0 &
% 7.54/1.77 | | | member(all_33_1, all_15_2) = 0 & $i(all_33_1)
% 7.54/1.77 | | |
% 7.54/1.77 | | | ALPHA: (20) implies:
% 7.54/1.77 | | | (21) ~ (all_33_0 = 0)
% 7.54/1.77 | | | (22) member(all_33_1, all_15_2) = 0
% 7.54/1.77 | | | (23) member(all_33_1, all_15_2) = all_33_0
% 7.54/1.77 | | |
% 7.54/1.77 | | | GROUND_INST: instantiating (3) with 0, all_33_0, all_15_2, all_33_1,
% 7.54/1.77 | | | simplifying with (22), (23) gives:
% 7.54/1.77 | | | (24) all_33_0 = 0
% 7.54/1.77 | | |
% 7.54/1.77 | | | REDUCE: (21), (24) imply:
% 7.54/1.77 | | | (25) $false
% 7.54/1.77 | | |
% 7.54/1.77 | | | CLOSE: (25) is inconsistent.
% 7.54/1.77 | | |
% 7.54/1.77 | | End of split
% 7.54/1.77 | |
% 7.54/1.77 | End of split
% 7.54/1.77 |
% 7.54/1.77 End of proof
% 7.54/1.77 % SZS output end Proof for theBenchmark
% 7.54/1.77
% 7.54/1.77 1233ms
%------------------------------------------------------------------------------