TSTP Solution File: SET095+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET095+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 : n014.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 15:23:46 EDT 2023
% Result : Theorem 6.48s 1.60s
% Output : Proof 7.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 14:27:32 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.47/1.02 Prover 1: Preprocessing ...
% 2.47/1.02 Prover 4: Preprocessing ...
% 2.47/1.06 Prover 6: Preprocessing ...
% 2.47/1.06 Prover 3: Preprocessing ...
% 2.47/1.06 Prover 2: Preprocessing ...
% 2.47/1.06 Prover 0: Preprocessing ...
% 2.47/1.06 Prover 5: Preprocessing ...
% 3.91/1.43 Prover 6: Proving ...
% 5.34/1.44 Prover 1: Constructing countermodel ...
% 5.34/1.45 Prover 3: Constructing countermodel ...
% 5.34/1.47 Prover 5: Proving ...
% 5.34/1.50 Prover 2: Proving ...
% 5.85/1.51 Prover 4: Constructing countermodel ...
% 5.85/1.52 Prover 0: Proving ...
% 6.48/1.59 Prover 6: proved (944ms)
% 6.48/1.60
% 6.48/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.48/1.60
% 6.48/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.48/1.60 Prover 0: stopped
% 6.48/1.62 Prover 3: proved (940ms)
% 6.48/1.62
% 6.48/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.48/1.62
% 6.48/1.62 Prover 5: stopped
% 6.48/1.62 Prover 2: stopped
% 6.48/1.64 Prover 7: Preprocessing ...
% 6.48/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.48/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.48/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.48/1.64 Prover 1: Found proof (size 16)
% 6.48/1.64 Prover 1: proved (990ms)
% 6.48/1.64 Prover 4: stopped
% 6.48/1.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.48/1.64 Prover 7: stopped
% 6.48/1.64 Prover 8: Preprocessing ...
% 6.48/1.64 Prover 10: Preprocessing ...
% 6.48/1.65 Prover 11: Preprocessing ...
% 6.48/1.66 Prover 10: stopped
% 6.48/1.66 Prover 13: Preprocessing ...
% 6.48/1.68 Prover 11: stopped
% 7.13/1.70 Prover 13: stopped
% 7.27/1.73 Prover 8: Warning: ignoring some quantifiers
% 7.27/1.74 Prover 8: Constructing countermodel ...
% 7.27/1.75 Prover 8: stopped
% 7.27/1.75
% 7.27/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.27/1.75
% 7.27/1.75 % SZS output start Proof for theBenchmark
% 7.27/1.75 Assumptions after simplification:
% 7.27/1.75 ---------------------------------
% 7.27/1.75
% 7.27/1.75 (singleton)
% 7.27/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) |
% 7.27/1.78 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 7.27/1.78 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~
% 7.27/1.78 $i(v1) | ~ $i(v0))
% 7.27/1.78
% 7.27/1.78 (subset)
% 7.27/1.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 7.27/1.78 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 7.27/1.78 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 7.27/1.78 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 7.27/1.78 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 7.27/1.78
% 7.27/1.78 (thI44)
% 7.27/1.78 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 7.27/1.78 singleton(v1) = v2 & subset(v2, v0) = v3 & member(v1, v0) = 0 & $i(v2) &
% 7.27/1.78 $i(v1) & $i(v0))
% 7.27/1.78
% 7.27/1.78 (function-axioms)
% 7.27/1.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.79 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 7.27/1.79 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.79 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 7.27/1.79 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 7.27/1.79 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.27/1.79 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 7.27/1.79 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.27/1.79 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 7.27/1.79 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.27/1.79 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 7.27/1.79 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.27/1.79 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.27/1.79 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 7.27/1.79 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 7.27/1.79 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 7.27/1.79 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 7.27/1.79 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 7.27/1.79 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 7.27/1.79 (power_set(v2) = v0))
% 7.27/1.79
% 7.27/1.79 Further assumptions not needed in the proof:
% 7.27/1.79 --------------------------------------------
% 7.27/1.79 difference, empty_set, equal_set, intersection, power_set, product, sum, union,
% 7.27/1.79 unordered_pair
% 7.27/1.79
% 7.27/1.79 Those formulas are unsatisfiable:
% 7.27/1.79 ---------------------------------
% 7.27/1.79
% 7.27/1.79 Begin of proof
% 7.27/1.79 |
% 7.27/1.79 | ALPHA: (subset) implies:
% 7.27/1.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 7.27/1.80 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 7.27/1.80 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 7.27/1.80 |
% 7.27/1.80 | ALPHA: (singleton) implies:
% 7.27/1.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1)
% 7.27/1.80 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 7.27/1.80 |
% 7.27/1.80 | ALPHA: (function-axioms) implies:
% 7.27/1.80 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.27/1.80 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 7.27/1.80 | = v0))
% 7.27/1.80 |
% 7.27/1.80 | DELTA: instantiating (thI44) with fresh symbols all_15_0, all_15_1, all_15_2,
% 7.27/1.80 | all_15_3 gives:
% 7.27/1.80 | (4) ~ (all_15_0 = 0) & singleton(all_15_2) = all_15_1 & subset(all_15_1,
% 7.27/1.80 | all_15_3) = all_15_0 & member(all_15_2, all_15_3) = 0 & $i(all_15_1)
% 7.27/1.80 | & $i(all_15_2) & $i(all_15_3)
% 7.27/1.80 |
% 7.27/1.80 | ALPHA: (4) implies:
% 7.27/1.80 | (5) ~ (all_15_0 = 0)
% 7.27/1.80 | (6) $i(all_15_3)
% 7.27/1.80 | (7) $i(all_15_2)
% 7.27/1.80 | (8) $i(all_15_1)
% 7.27/1.80 | (9) member(all_15_2, all_15_3) = 0
% 7.27/1.80 | (10) subset(all_15_1, all_15_3) = all_15_0
% 7.27/1.80 | (11) singleton(all_15_2) = all_15_1
% 7.27/1.80 |
% 7.27/1.80 | GROUND_INST: instantiating (1) with all_15_1, all_15_3, all_15_0, simplifying
% 7.27/1.80 | with (6), (8), (10) gives:
% 7.27/1.80 | (12) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 7.27/1.80 | all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0))
% 7.27/1.80 |
% 7.27/1.80 | BETA: splitting (12) gives:
% 7.27/1.80 |
% 7.27/1.80 | Case 1:
% 7.27/1.80 | |
% 7.27/1.80 | | (13) all_15_0 = 0
% 7.27/1.80 | |
% 7.27/1.80 | | REDUCE: (5), (13) imply:
% 7.27/1.80 | | (14) $false
% 7.27/1.80 | |
% 7.27/1.80 | | CLOSE: (14) is inconsistent.
% 7.27/1.81 | |
% 7.27/1.81 | Case 2:
% 7.27/1.81 | |
% 7.73/1.81 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = 0
% 7.73/1.81 | | & member(v0, all_15_3) = v1 & $i(v0))
% 7.73/1.81 | |
% 7.73/1.81 | | DELTA: instantiating (15) with fresh symbols all_24_0, all_24_1 gives:
% 7.73/1.81 | | (16) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = 0 &
% 7.73/1.81 | | member(all_24_1, all_15_3) = all_24_0 & $i(all_24_1)
% 7.73/1.81 | |
% 7.73/1.81 | | ALPHA: (16) implies:
% 7.73/1.81 | | (17) ~ (all_24_0 = 0)
% 7.73/1.81 | | (18) $i(all_24_1)
% 7.73/1.81 | | (19) member(all_24_1, all_15_3) = all_24_0
% 7.73/1.81 | | (20) member(all_24_1, all_15_1) = 0
% 7.73/1.81 | |
% 7.73/1.81 | | GROUND_INST: instantiating (2) with all_24_1, all_15_2, all_15_1,
% 7.73/1.81 | | simplifying with (7), (11), (18), (20) gives:
% 7.73/1.81 | | (21) all_24_1 = all_15_2
% 7.73/1.81 | |
% 7.73/1.81 | | REDUCE: (19), (21) imply:
% 7.73/1.81 | | (22) member(all_15_2, all_15_3) = all_24_0
% 7.73/1.81 | |
% 7.73/1.81 | | GROUND_INST: instantiating (3) with 0, all_24_0, all_15_3, all_15_2,
% 7.73/1.81 | | simplifying with (9), (22) gives:
% 7.73/1.81 | | (23) all_24_0 = 0
% 7.73/1.81 | |
% 7.73/1.81 | | REDUCE: (17), (23) imply:
% 7.73/1.81 | | (24) $false
% 7.73/1.81 | |
% 7.73/1.81 | | CLOSE: (24) is inconsistent.
% 7.73/1.81 | |
% 7.73/1.81 | End of split
% 7.73/1.81 |
% 7.73/1.81 End of proof
% 7.73/1.81 % SZS output end Proof for theBenchmark
% 7.73/1.81
% 7.73/1.81 1185ms
%------------------------------------------------------------------------------