TSTP Solution File: SET687+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET687+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 : n013.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 15:26:00 EDT 2023
% Result : Theorem 6.04s 1.55s
% Output : Proof 7.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET687+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:18:32 EDT 2023
% 0.13/0.34 % 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 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 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 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 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 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 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
% 1.91/1.04 Prover 1: Preprocessing ...
% 1.91/1.04 Prover 4: Preprocessing ...
% 2.65/1.09 Prover 5: Preprocessing ...
% 2.65/1.09 Prover 0: Preprocessing ...
% 2.65/1.09 Prover 3: Preprocessing ...
% 2.65/1.09 Prover 2: Preprocessing ...
% 2.65/1.09 Prover 6: Preprocessing ...
% 4.70/1.44 Prover 6: Proving ...
% 4.70/1.44 Prover 5: Proving ...
% 4.70/1.46 Prover 2: Proving ...
% 4.70/1.46 Prover 1: Constructing countermodel ...
% 4.70/1.47 Prover 3: Constructing countermodel ...
% 5.53/1.50 Prover 0: Proving ...
% 5.53/1.52 Prover 4: Constructing countermodel ...
% 6.04/1.55 Prover 3: proved (924ms)
% 6.04/1.55
% 6.04/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.04/1.55
% 6.22/1.57 Prover 6: proved (922ms)
% 6.22/1.57
% 6.22/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.22/1.57
% 6.22/1.57 Prover 0: stopped
% 6.22/1.57 Prover 2: stopped
% 6.22/1.57 Prover 5: stopped
% 6.22/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.22/1.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.22/1.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.22/1.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.22/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.22/1.60 Prover 10: Preprocessing ...
% 6.22/1.61 Prover 7: Preprocessing ...
% 6.22/1.62 Prover 1: Found proof (size 13)
% 6.22/1.62 Prover 1: proved (998ms)
% 6.22/1.62 Prover 4: stopped
% 6.22/1.62 Prover 8: Preprocessing ...
% 6.61/1.63 Prover 11: Preprocessing ...
% 6.61/1.63 Prover 10: stopped
% 6.61/1.63 Prover 13: Preprocessing ...
% 6.61/1.64 Prover 7: stopped
% 6.85/1.66 Prover 11: stopped
% 6.85/1.67 Prover 13: stopped
% 6.85/1.71 Prover 8: Warning: ignoring some quantifiers
% 6.85/1.73 Prover 8: Constructing countermodel ...
% 7.25/1.73 Prover 8: stopped
% 7.25/1.73
% 7.25/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.25/1.74
% 7.25/1.74 % SZS output start Proof for theBenchmark
% 7.25/1.74 Assumptions after simplification:
% 7.25/1.74 ---------------------------------
% 7.25/1.74
% 7.25/1.74 (subset)
% 7.25/1.77 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.25/1.77 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.25/1.77 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.25/1.77 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.25/1.77 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.25/1.77
% 7.25/1.77 (thI01)
% 7.25/1.77 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, v0) = v1 & $i(v0))
% 7.25/1.77
% 7.25/1.77 (function-axioms)
% 7.47/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.47/1.78 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.47/1.78 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.47/1.78 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.47/1.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.47/1.78 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.47/1.78 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 7.47/1.78 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.47/1.78 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 7.47/1.78 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.47/1.78 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.47/1.78 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.47/1.78 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.47/1.78 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.47/1.78 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 7.47/1.78 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 7.47/1.78 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 7.47/1.78 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 7.47/1.78 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 7.47/1.78 (power_set(v2) = v0))
% 7.47/1.78
% 7.47/1.78 Further assumptions not needed in the proof:
% 7.47/1.78 --------------------------------------------
% 7.47/1.78 difference, empty_set, equal_set, intersection, power_set, product, singleton,
% 7.47/1.78 sum, union, unordered_pair
% 7.47/1.78
% 7.47/1.78 Those formulas are unsatisfiable:
% 7.47/1.78 ---------------------------------
% 7.47/1.78
% 7.47/1.78 Begin of proof
% 7.47/1.78 |
% 7.47/1.79 | ALPHA: (subset) implies:
% 7.47/1.79 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.47/1.79 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.47/1.79 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.47/1.79 |
% 7.47/1.79 | ALPHA: (function-axioms) implies:
% 7.47/1.79 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.47/1.79 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.47/1.79 | = v0))
% 7.47/1.79 |
% 7.47/1.79 | DELTA: instantiating (thI01) with fresh symbols all_15_0, all_15_1 gives:
% 7.47/1.79 | (3) ~ (all_15_0 = 0) & subset(all_15_1, all_15_1) = all_15_0 &
% 7.47/1.79 | $i(all_15_1)
% 7.47/1.79 |
% 7.47/1.79 | ALPHA: (3) implies:
% 7.47/1.79 | (4) ~ (all_15_0 = 0)
% 7.47/1.79 | (5) $i(all_15_1)
% 7.47/1.79 | (6) subset(all_15_1, all_15_1) = all_15_0
% 7.47/1.79 |
% 7.47/1.79 | GROUND_INST: instantiating (1) with all_15_1, all_15_1, all_15_0, simplifying
% 7.47/1.79 | with (5), (6) gives:
% 7.47/1.80 | (7) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.47/1.80 | all_15_1) = v1 & member(v0, all_15_1) = 0 & $i(v0))
% 7.47/1.80 |
% 7.47/1.80 | BETA: splitting (7) gives:
% 7.47/1.80 |
% 7.47/1.80 | Case 1:
% 7.47/1.80 | |
% 7.47/1.80 | | (8) all_15_0 = 0
% 7.47/1.80 | |
% 7.47/1.80 | | REDUCE: (4), (8) imply:
% 7.47/1.80 | | (9) $false
% 7.47/1.80 | |
% 7.47/1.80 | | CLOSE: (9) is inconsistent.
% 7.47/1.80 | |
% 7.47/1.80 | Case 2:
% 7.47/1.80 | |
% 7.47/1.80 | | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) =
% 7.47/1.80 | | v1 & member(v0, all_15_1) = 0 & $i(v0))
% 7.47/1.80 | |
% 7.47/1.80 | | DELTA: instantiating (10) with fresh symbols all_24_0, all_24_1 gives:
% 7.47/1.80 | | (11) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = all_24_0 &
% 7.47/1.80 | | member(all_24_1, all_15_1) = 0 & $i(all_24_1)
% 7.47/1.80 | |
% 7.47/1.80 | | ALPHA: (11) implies:
% 7.47/1.80 | | (12) ~ (all_24_0 = 0)
% 7.47/1.80 | | (13) member(all_24_1, all_15_1) = 0
% 7.47/1.80 | | (14) member(all_24_1, all_15_1) = all_24_0
% 7.47/1.80 | |
% 7.47/1.80 | | GROUND_INST: instantiating (2) with 0, all_24_0, all_15_1, all_24_1,
% 7.47/1.80 | | simplifying with (13), (14) gives:
% 7.47/1.80 | | (15) all_24_0 = 0
% 7.47/1.80 | |
% 7.47/1.80 | | REDUCE: (12), (15) imply:
% 7.47/1.80 | | (16) $false
% 7.47/1.80 | |
% 7.47/1.80 | | CLOSE: (16) is inconsistent.
% 7.47/1.80 | |
% 7.47/1.80 | End of split
% 7.47/1.80 |
% 7.47/1.80 End of proof
% 7.47/1.80 % SZS output end Proof for theBenchmark
% 7.47/1.80
% 7.47/1.80 1200ms
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