TSTP Solution File: SET002+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET002+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 : n001.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 15:23:01 EDT 2023
% Result : Theorem 4.42s 1.34s
% Output : Proof 5.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.34 % Computer : n001.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Sat Aug 26 09:30:15 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.83/0.97 Prover 4: Preprocessing ...
% 1.83/0.97 Prover 1: Preprocessing ...
% 2.32/1.02 Prover 2: Preprocessing ...
% 2.32/1.02 Prover 3: Preprocessing ...
% 2.32/1.02 Prover 6: Preprocessing ...
% 2.32/1.02 Prover 5: Preprocessing ...
% 2.32/1.02 Prover 0: Preprocessing ...
% 3.95/1.22 Prover 3: Warning: ignoring some quantifiers
% 3.95/1.22 Prover 5: Proving ...
% 3.95/1.22 Prover 6: Proving ...
% 3.95/1.23 Prover 1: Warning: ignoring some quantifiers
% 3.95/1.23 Prover 2: Proving ...
% 3.95/1.23 Prover 1: Constructing countermodel ...
% 3.95/1.24 Prover 4: Warning: ignoring some quantifiers
% 3.95/1.24 Prover 3: Constructing countermodel ...
% 3.95/1.25 Prover 4: Constructing countermodel ...
% 3.95/1.25 Prover 0: Proving ...
% 4.42/1.34 Prover 3: proved (705ms)
% 4.42/1.34
% 4.42/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/1.34
% 4.42/1.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.42/1.34 Prover 2: stopped
% 4.42/1.34 Prover 0: stopped
% 4.42/1.35 Prover 5: stopped
% 4.42/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.42/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.42/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.42/1.35 Prover 6: proved (719ms)
% 4.42/1.35
% 4.42/1.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/1.35
% 4.42/1.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.92/1.37 Prover 11: Preprocessing ...
% 4.92/1.37 Prover 4: Found proof (size 14)
% 4.92/1.37 Prover 4: proved (740ms)
% 4.92/1.37 Prover 1: stopped
% 4.92/1.37 Prover 7: Preprocessing ...
% 4.92/1.38 Prover 10: Preprocessing ...
% 4.92/1.38 Prover 8: Preprocessing ...
% 4.92/1.39 Prover 13: Preprocessing ...
% 4.92/1.39 Prover 10: stopped
% 4.92/1.39 Prover 7: stopped
% 4.92/1.40 Prover 13: stopped
% 4.92/1.41 Prover 11: stopped
% 4.92/1.43 Prover 8: Warning: ignoring some quantifiers
% 4.92/1.44 Prover 8: Constructing countermodel ...
% 4.92/1.44 Prover 8: stopped
% 4.92/1.44
% 4.92/1.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.92/1.44
% 4.92/1.45 % SZS output start Proof for theBenchmark
% 4.92/1.45 Assumptions after simplification:
% 4.92/1.45 ---------------------------------
% 4.92/1.45
% 4.92/1.45 (equal_defn)
% 4.92/1.48 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) |
% 4.92/1.48 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i]
% 4.92/1.48 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 4.92/1.48 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1:
% 4.92/1.48 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 4.92/1.48
% 4.92/1.48 (prove_idempotency_of_union)
% 5.51/1.48 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & union(v0, v0) = v1 & $i(v1) &
% 5.51/1.48 $i(v0))
% 5.51/1.48
% 5.51/1.48 (subset_union)
% 5.51/1.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0, v1) = v2) |
% 5.51/1.48 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 5.51/1.48 & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 5.51/1.48 | union(v0, v1) = v1)
% 5.51/1.48
% 5.51/1.48 Further assumptions not needed in the proof:
% 5.51/1.48 --------------------------------------------
% 5.51/1.48 commutativity_of_union, equal_member_defn, reflexivity_of_subset, subset_defn,
% 5.51/1.48 union_defn
% 5.51/1.48
% 5.51/1.48 Those formulas are unsatisfiable:
% 5.51/1.48 ---------------------------------
% 5.51/1.48
% 5.51/1.48 Begin of proof
% 5.51/1.49 |
% 5.51/1.49 | ALPHA: (subset_union) implies:
% 5.51/1.49 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (union(v0, v1)
% 5.51/1.49 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 5.51/1.49 | subset(v0, v1) = v3))
% 5.51/1.49 |
% 5.51/1.49 | ALPHA: (equal_defn) implies:
% 5.51/1.49 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~
% 5.51/1.49 | $i(v0))
% 5.51/1.49 |
% 5.51/1.49 | DELTA: instantiating (prove_idempotency_of_union) with fresh symbols all_9_0,
% 5.51/1.49 | all_9_1 gives:
% 5.51/1.49 | (3) ~ (all_9_0 = all_9_1) & union(all_9_1, all_9_1) = all_9_0 &
% 5.51/1.49 | $i(all_9_0) & $i(all_9_1)
% 5.51/1.49 |
% 5.51/1.49 | ALPHA: (3) implies:
% 5.51/1.49 | (4) ~ (all_9_0 = all_9_1)
% 5.51/1.49 | (5) $i(all_9_1)
% 5.51/1.49 | (6) union(all_9_1, all_9_1) = all_9_0
% 5.51/1.49 |
% 5.51/1.49 | GROUND_INST: instantiating (1) with all_9_1, all_9_1, all_9_0, simplifying
% 5.51/1.49 | with (5), (6) gives:
% 5.51/1.49 | (7) all_9_0 = all_9_1 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1,
% 5.51/1.49 | all_9_1) = v0)
% 5.51/1.49 |
% 5.51/1.49 | BETA: splitting (7) gives:
% 5.51/1.49 |
% 5.51/1.49 | Case 1:
% 5.51/1.49 | |
% 5.51/1.49 | | (8) all_9_0 = all_9_1
% 5.51/1.49 | |
% 5.51/1.50 | | REDUCE: (4), (8) imply:
% 5.51/1.50 | | (9) $false
% 5.51/1.50 | |
% 5.51/1.50 | | CLOSE: (9) is inconsistent.
% 5.51/1.50 | |
% 5.51/1.50 | Case 2:
% 5.51/1.50 | |
% 5.51/1.50 | | (10) ? [v0: int] : ( ~ (v0 = 0) & subset(all_9_1, all_9_1) = v0)
% 5.51/1.50 | |
% 5.51/1.50 | | DELTA: instantiating (10) with fresh symbol all_23_0 gives:
% 5.51/1.50 | | (11) ~ (all_23_0 = 0) & subset(all_9_1, all_9_1) = all_23_0
% 5.51/1.50 | |
% 5.51/1.50 | | ALPHA: (11) implies:
% 5.51/1.50 | | (12) ~ (all_23_0 = 0)
% 5.51/1.50 | | (13) subset(all_9_1, all_9_1) = all_23_0
% 5.51/1.50 | |
% 5.51/1.50 | | GROUND_INST: instantiating (2) with all_9_1, all_23_0, simplifying with (5),
% 5.51/1.50 | | (13) gives:
% 5.51/1.50 | | (14) all_23_0 = 0
% 5.51/1.50 | |
% 5.51/1.50 | | REDUCE: (12), (14) imply:
% 5.51/1.50 | | (15) $false
% 5.51/1.50 | |
% 5.51/1.50 | | CLOSE: (15) is inconsistent.
% 5.51/1.50 | |
% 5.51/1.50 | End of split
% 5.51/1.50 |
% 5.51/1.50 End of proof
% 5.51/1.50 % SZS output end Proof for theBenchmark
% 5.51/1.50
% 5.51/1.50 890ms
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