TSTP Solution File: SET605+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET605+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 : n028.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 15:25:33 EDT 2023
% Result : Theorem 5.41s 1.52s
% Output : Proof 6.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 15:09:37 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/1.03 Prover 4: Preprocessing ...
% 2.26/1.03 Prover 1: Preprocessing ...
% 2.52/1.09 Prover 6: Preprocessing ...
% 2.52/1.09 Prover 2: Preprocessing ...
% 2.52/1.09 Prover 0: Preprocessing ...
% 2.52/1.09 Prover 3: Preprocessing ...
% 2.52/1.09 Prover 5: Preprocessing ...
% 4.45/1.37 Prover 1: Warning: ignoring some quantifiers
% 4.45/1.38 Prover 3: Warning: ignoring some quantifiers
% 4.45/1.39 Prover 4: Warning: ignoring some quantifiers
% 4.45/1.39 Prover 1: Constructing countermodel ...
% 4.45/1.39 Prover 3: Constructing countermodel ...
% 4.45/1.41 Prover 6: Proving ...
% 4.45/1.41 Prover 5: Proving ...
% 4.45/1.41 Prover 4: Constructing countermodel ...
% 4.45/1.41 Prover 2: Proving ...
% 4.45/1.43 Prover 0: Proving ...
% 5.41/1.52 Prover 3: proved (891ms)
% 5.41/1.52
% 5.41/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/1.52
% 5.41/1.52 Prover 2: stopped
% 5.41/1.53 Prover 6: stopped
% 5.41/1.53 Prover 5: stopped
% 5.41/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.41/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.41/1.54 Prover 0: proved (914ms)
% 5.41/1.54
% 5.41/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/1.54
% 5.41/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.41/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.41/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.41/1.56 Prover 11: Preprocessing ...
% 5.41/1.57 Prover 7: Preprocessing ...
% 5.41/1.59 Prover 10: Preprocessing ...
% 5.41/1.59 Prover 8: Preprocessing ...
% 5.41/1.59 Prover 13: Preprocessing ...
% 5.41/1.60 Prover 4: Found proof (size 18)
% 5.41/1.60 Prover 4: proved (978ms)
% 5.41/1.61 Prover 1: stopped
% 5.41/1.61 Prover 10: stopped
% 5.41/1.61 Prover 11: stopped
% 5.41/1.62 Prover 13: stopped
% 5.41/1.63 Prover 7: stopped
% 5.41/1.66 Prover 8: Warning: ignoring some quantifiers
% 5.41/1.67 Prover 8: Constructing countermodel ...
% 5.41/1.68 Prover 8: stopped
% 5.41/1.68
% 5.41/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/1.68
% 5.41/1.68 % SZS output start Proof for theBenchmark
% 5.41/1.68 Assumptions after simplification:
% 5.41/1.68 ---------------------------------
% 5.41/1.68
% 5.41/1.68 (commutativity_of_union)
% 6.67/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~ $i(v1)
% 6.67/1.71 | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 6.67/1.71 ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (union(v1, v0)
% 6.67/1.71 = v2 & $i(v2)))
% 6.67/1.71
% 6.67/1.71 (difference_empty_set)
% 6.67/1.71 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 6.67/1.71 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 =
% 6.67/1.71 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 6.67/1.71 (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~
% 6.67/1.71 (v3 = empty_set) & difference(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : !
% 6.67/1.71 [v1: $i] : ( ~ (difference(v0, v1) = empty_set) | ~ $i(v1) | ~ $i(v0) |
% 6.67/1.71 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 6.67/1.71 ~ $i(v1) | ~ $i(v0) | difference(v0, v1) = empty_set)
% 6.67/1.71
% 6.67/1.71 (prove_th76)
% 6.67/1.72 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 6.67/1.72 (v3 = empty_set) & difference(v0, v2) = v3 & union(v0, v1) = v2 & $i(v3) &
% 6.67/1.72 $i(v2) & $i(v1) & $i(v0))
% 6.67/1.72
% 6.67/1.72 (subset_of_union)
% 6.67/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1)
% 6.67/1.72 | ~ $i(v0) | subset(v0, v2) = 0)
% 6.67/1.72
% 6.67/1.72 (function-axioms)
% 6.67/1.72 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 6.67/1.72 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) &
% 6.67/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 6.67/1.72 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 6.67/1.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 6.67/1.72 (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 6.67/1.72 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 6.67/1.72 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 6.67/1.72 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 6.67/1.72 (empty(v2) = v0))
% 6.67/1.72
% 6.67/1.72 Further assumptions not needed in the proof:
% 6.67/1.72 --------------------------------------------
% 6.67/1.72 difference_defn, empty_defn, empty_set_defn, equal_defn, equal_member_defn,
% 6.67/1.72 reflexivity_of_subset, subset_defn, union_defn
% 6.67/1.72
% 6.67/1.72 Those formulas are unsatisfiable:
% 6.67/1.72 ---------------------------------
% 6.67/1.72
% 6.67/1.72 Begin of proof
% 6.67/1.72 |
% 6.67/1.73 | ALPHA: (difference_empty_set) implies:
% 6.67/1.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~
% 6.67/1.73 | (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 6.67/1.73 | ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.67/1.73 |
% 6.67/1.73 | ALPHA: (commutativity_of_union) implies:
% 6.67/1.73 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v1, v0) = v2) | ~
% 6.67/1.73 | $i(v1) | ~ $i(v0) | (union(v0, v1) = v2 & $i(v2)))
% 6.67/1.73 |
% 6.67/1.73 | ALPHA: (prove_th76) implies:
% 6.67/1.73 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 6.67/1.73 | empty_set) & difference(v0, v2) = v3 & union(v0, v1) = v2 & $i(v3)
% 6.67/1.73 | & $i(v2) & $i(v1) & $i(v0))
% 6.67/1.73 |
% 6.67/1.73 | ALPHA: (function-axioms) implies:
% 6.67/1.73 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 6.67/1.73 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 6.67/1.73 | = v0))
% 6.67/1.73 |
% 6.67/1.73 | DELTA: instantiating (3) with fresh symbols all_14_0, all_14_1, all_14_2,
% 6.67/1.73 | all_14_3 gives:
% 6.67/1.73 | (5) ~ (all_14_0 = empty_set) & difference(all_14_3, all_14_1) = all_14_0 &
% 6.67/1.73 | union(all_14_3, all_14_2) = all_14_1 & $i(all_14_0) & $i(all_14_1) &
% 6.67/1.73 | $i(all_14_2) & $i(all_14_3)
% 6.67/1.73 |
% 6.67/1.73 | ALPHA: (5) implies:
% 6.67/1.73 | (6) ~ (all_14_0 = empty_set)
% 6.67/1.73 | (7) $i(all_14_3)
% 6.67/1.73 | (8) $i(all_14_2)
% 6.67/1.73 | (9) union(all_14_3, all_14_2) = all_14_1
% 6.67/1.73 | (10) difference(all_14_3, all_14_1) = all_14_0
% 6.67/1.73 |
% 6.67/1.74 | GROUND_INST: instantiating (2) with all_14_2, all_14_3, all_14_1, simplifying
% 6.67/1.74 | with (7), (8), (9) gives:
% 6.67/1.74 | (11) union(all_14_2, all_14_3) = all_14_1 & $i(all_14_1)
% 6.67/1.74 |
% 6.67/1.74 | ALPHA: (11) implies:
% 6.67/1.74 | (12) $i(all_14_1)
% 6.67/1.74 |
% 6.67/1.74 | GROUND_INST: instantiating (subset_of_union) with all_14_3, all_14_2,
% 6.67/1.74 | all_14_1, simplifying with (7), (8), (9) gives:
% 6.67/1.74 | (13) subset(all_14_3, all_14_1) = 0
% 6.67/1.74 |
% 6.67/1.74 | GROUND_INST: instantiating (1) with all_14_3, all_14_1, all_14_0, simplifying
% 6.67/1.74 | with (7), (10), (12) gives:
% 6.67/1.74 | (14) all_14_0 = empty_set | ? [v0: int] : ( ~ (v0 = 0) & subset(all_14_3,
% 6.67/1.74 | all_14_1) = v0)
% 6.67/1.74 |
% 6.67/1.74 | BETA: splitting (14) gives:
% 6.67/1.74 |
% 6.67/1.74 | Case 1:
% 6.67/1.74 | |
% 6.67/1.74 | | (15) all_14_0 = empty_set
% 6.67/1.74 | |
% 6.67/1.74 | | REDUCE: (6), (15) imply:
% 6.67/1.74 | | (16) $false
% 6.67/1.74 | |
% 6.67/1.74 | | CLOSE: (16) is inconsistent.
% 6.67/1.74 | |
% 6.67/1.74 | Case 2:
% 6.67/1.74 | |
% 6.67/1.74 | | (17) ? [v0: int] : ( ~ (v0 = 0) & subset(all_14_3, all_14_1) = v0)
% 6.67/1.74 | |
% 6.67/1.74 | | DELTA: instantiating (17) with fresh symbol all_27_0 gives:
% 6.67/1.74 | | (18) ~ (all_27_0 = 0) & subset(all_14_3, all_14_1) = all_27_0
% 6.67/1.74 | |
% 6.67/1.74 | | ALPHA: (18) implies:
% 6.67/1.74 | | (19) ~ (all_27_0 = 0)
% 6.67/1.74 | | (20) subset(all_14_3, all_14_1) = all_27_0
% 6.67/1.74 | |
% 6.67/1.74 | | GROUND_INST: instantiating (4) with 0, all_27_0, all_14_1, all_14_3,
% 6.67/1.74 | | simplifying with (13), (20) gives:
% 6.67/1.74 | | (21) all_27_0 = 0
% 6.67/1.74 | |
% 6.67/1.74 | | REDUCE: (19), (21) imply:
% 6.67/1.74 | | (22) $false
% 6.67/1.74 | |
% 6.67/1.74 | | CLOSE: (22) is inconsistent.
% 6.67/1.74 | |
% 6.67/1.74 | End of split
% 6.67/1.74 |
% 6.67/1.74 End of proof
% 6.67/1.74 % SZS output end Proof for theBenchmark
% 6.67/1.74
% 6.67/1.74 1140ms
%------------------------------------------------------------------------------