TSTP Solution File: SET618+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET618+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 : 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 15:25:39 EDT 2023
% Result : Theorem 5.30s 1.49s
% Output : Proof 6.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % 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 11:03:02 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.98/1.01 Prover 4: Preprocessing ...
% 1.98/1.01 Prover 1: Preprocessing ...
% 2.42/1.05 Prover 5: Preprocessing ...
% 2.42/1.05 Prover 2: Preprocessing ...
% 2.42/1.05 Prover 3: Preprocessing ...
% 2.42/1.05 Prover 0: Preprocessing ...
% 2.42/1.05 Prover 6: Preprocessing ...
% 3.96/1.31 Prover 1: Warning: ignoring some quantifiers
% 3.96/1.33 Prover 5: Proving ...
% 3.96/1.33 Prover 1: Constructing countermodel ...
% 3.96/1.33 Prover 6: Proving ...
% 4.41/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.41/1.34 Prover 2: Proving ...
% 4.41/1.34 Prover 3: Constructing countermodel ...
% 4.41/1.35 Prover 4: Warning: ignoring some quantifiers
% 4.41/1.35 Prover 0: Proving ...
% 4.41/1.36 Prover 4: Constructing countermodel ...
% 5.30/1.48 Prover 3: gave up
% 5.30/1.48 Prover 1: gave up
% 5.30/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.30/1.48 Prover 0: proved (831ms)
% 5.30/1.48
% 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/1.49
% 5.30/1.49 Prover 2: proved (826ms)
% 5.30/1.49
% 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/1.49
% 5.30/1.49 Prover 5: proved (820ms)
% 5.30/1.49
% 5.30/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/1.49
% 5.30/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.30/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.30/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.30/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.30/1.49 Prover 6: stopped
% 5.30/1.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.30/1.50 Prover 4: Found proof (size 19)
% 5.30/1.50 Prover 4: proved (839ms)
% 5.30/1.53 Prover 10: Preprocessing ...
% 5.30/1.53 Prover 11: Preprocessing ...
% 5.30/1.53 Prover 13: Preprocessing ...
% 5.30/1.53 Prover 8: Preprocessing ...
% 5.30/1.54 Prover 7: Preprocessing ...
% 5.30/1.54 Prover 16: Preprocessing ...
% 5.76/1.55 Prover 10: stopped
% 5.76/1.56 Prover 13: stopped
% 5.76/1.56 Prover 7: stopped
% 5.76/1.57 Prover 16: stopped
% 5.76/1.57 Prover 11: stopped
% 5.98/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.19/1.64 Prover 8: Constructing countermodel ...
% 6.19/1.65 Prover 8: stopped
% 6.19/1.65
% 6.19/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.19/1.65
% 6.19/1.65 % SZS output start Proof for theBenchmark
% 6.25/1.66 Assumptions after simplification:
% 6.25/1.66 ---------------------------------
% 6.25/1.66
% 6.25/1.66 (idempotency_of_union)
% 6.25/1.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (union(v0, v0) = v1) | ~ $i(v0))
% 6.25/1.68
% 6.25/1.68 (prove_th93)
% 6.25/1.69 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 6.25/1.69 symmetric_difference(v0, v0) = v1 & $i(v1) & $i(v0))
% 6.25/1.69
% 6.25/1.69 (self_difference_is_empty_set)
% 6.25/1.69 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~
% 6.25/1.69 (difference(v0, v0) = v1) | ~ $i(v0))
% 6.25/1.69
% 6.25/1.69 (symmetric_difference_defn)
% 6.25/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) =
% 6.25/1.69 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1,
% 6.25/1.69 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) &
% 6.25/1.69 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 6.25/1.69 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 6.25/1.69 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 &
% 6.25/1.69 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : !
% 6.25/1.69 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 6.25/1.69 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4
% 6.25/1.69 & union(v2, v4) = v3 & $i(v4) & $i(v3)))
% 6.25/1.69
% 6.25/1.70 (function-axioms)
% 6.25/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.25/1.70 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 6.25/1.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 6.25/1.70 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 6.25/1.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.25/1.70 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) =
% 6.25/1.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 6.25/1.70 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] :
% 6.25/1.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) |
% 6.25/1.70 ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.25/1.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 6.25/1.70 (empty(v2) = v0))
% 6.25/1.70
% 6.25/1.70 Further assumptions not needed in the proof:
% 6.25/1.70 --------------------------------------------
% 6.25/1.70 commutativity_of_symmetric_difference, commutativity_of_union, empty_defn,
% 6.25/1.70 empty_set_defn, equal_defn, equal_member_defn, reflexivity_of_subset,
% 6.25/1.70 subset_defn
% 6.25/1.70
% 6.25/1.70 Those formulas are unsatisfiable:
% 6.25/1.70 ---------------------------------
% 6.25/1.70
% 6.25/1.70 Begin of proof
% 6.25/1.70 |
% 6.25/1.70 | ALPHA: (symmetric_difference_defn) implies:
% 6.25/1.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0,
% 6.25/1.71 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 6.25/1.71 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) =
% 6.25/1.71 | v2 & $i(v4) & $i(v3) & $i(v2)))
% 6.25/1.71 |
% 6.25/1.71 | ALPHA: (self_difference_is_empty_set) implies:
% 6.25/1.71 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = empty_set | ~ (difference(v0, v0) =
% 6.25/1.71 | v1) | ~ $i(v0))
% 6.25/1.71 |
% 6.25/1.71 | ALPHA: (prove_th93) implies:
% 6.25/1.71 | (3) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = empty_set) &
% 6.25/1.71 | symmetric_difference(v0, v0) = v1 & $i(v1) & $i(v0))
% 6.25/1.71 |
% 6.25/1.71 | ALPHA: (function-axioms) implies:
% 6.25/1.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.25/1.71 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 6.25/1.71 |
% 6.25/1.71 | DELTA: instantiating (3) with fresh symbols all_14_0, all_14_1 gives:
% 6.25/1.71 | (5) ~ (all_14_0 = empty_set) & symmetric_difference(all_14_1, all_14_1) =
% 6.25/1.71 | all_14_0 & $i(all_14_0) & $i(all_14_1)
% 6.25/1.71 |
% 6.25/1.71 | ALPHA: (5) implies:
% 6.25/1.71 | (6) ~ (all_14_0 = empty_set)
% 6.25/1.71 | (7) $i(all_14_1)
% 6.25/1.71 | (8) symmetric_difference(all_14_1, all_14_1) = all_14_0
% 6.25/1.71 |
% 6.25/1.71 | GROUND_INST: instantiating (1) with all_14_1, all_14_1, all_14_0, simplifying
% 6.25/1.71 | with (7), (8) gives:
% 6.25/1.71 | (9) ? [v0: $i] : ? [v1: $i] : (difference(all_14_1, all_14_1) = v1 &
% 6.25/1.71 | difference(all_14_1, all_14_1) = v0 & union(v0, v1) = all_14_0 &
% 6.25/1.71 | $i(v1) & $i(v0) & $i(all_14_0))
% 6.25/1.71 |
% 6.25/1.72 | DELTA: instantiating (9) with fresh symbols all_22_0, all_22_1 gives:
% 6.25/1.72 | (10) difference(all_14_1, all_14_1) = all_22_0 & difference(all_14_1,
% 6.25/1.72 | all_14_1) = all_22_1 & union(all_22_1, all_22_0) = all_14_0 &
% 6.25/1.72 | $i(all_22_0) & $i(all_22_1) & $i(all_14_0)
% 6.25/1.72 |
% 6.25/1.72 | ALPHA: (10) implies:
% 6.25/1.72 | (11) $i(all_22_0)
% 6.25/1.72 | (12) union(all_22_1, all_22_0) = all_14_0
% 6.25/1.72 | (13) difference(all_14_1, all_14_1) = all_22_1
% 6.25/1.72 | (14) difference(all_14_1, all_14_1) = all_22_0
% 6.25/1.72 |
% 6.25/1.72 | GROUND_INST: instantiating (4) with all_22_1, all_22_0, all_14_1, all_14_1,
% 6.25/1.72 | simplifying with (13), (14) gives:
% 6.25/1.72 | (15) all_22_0 = all_22_1
% 6.25/1.72 |
% 6.25/1.72 | REDUCE: (12), (15) imply:
% 6.25/1.72 | (16) union(all_22_1, all_22_1) = all_14_0
% 6.25/1.72 |
% 6.25/1.72 | REDUCE: (11), (15) imply:
% 6.56/1.72 | (17) $i(all_22_1)
% 6.56/1.72 |
% 6.56/1.72 | GROUND_INST: instantiating (idempotency_of_union) with all_22_1, all_14_0,
% 6.56/1.72 | simplifying with (16), (17) gives:
% 6.56/1.72 | (18) all_22_1 = all_14_0
% 6.56/1.72 |
% 6.56/1.72 | GROUND_INST: instantiating (2) with all_14_1, all_22_1, simplifying with (7),
% 6.56/1.72 | (13) gives:
% 6.56/1.72 | (19) all_22_1 = empty_set
% 6.56/1.72 |
% 6.56/1.72 | COMBINE_EQS: (18), (19) imply:
% 6.56/1.72 | (20) all_14_0 = empty_set
% 6.56/1.72 |
% 6.56/1.72 | SIMP: (20) implies:
% 6.56/1.72 | (21) all_14_0 = empty_set
% 6.56/1.72 |
% 6.56/1.72 | REDUCE: (6), (21) imply:
% 6.56/1.72 | (22) $false
% 6.56/1.72 |
% 6.56/1.72 | CLOSE: (22) is inconsistent.
% 6.56/1.72 |
% 6.56/1.72 End of proof
% 6.56/1.72 % SZS output end Proof for theBenchmark
% 6.56/1.72
% 6.56/1.72 1087ms
%------------------------------------------------------------------------------