TSTP Solution File: SET626+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET626+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 15:25:43 EDT 2023
% Result : Theorem 3.85s 1.43s
% Output : Proof 5.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 16:29:22 EDT 2023
% 0.12/0.34 % 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.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.60/1.00 Prover 4: Preprocessing ...
% 1.60/1.00 Prover 1: Preprocessing ...
% 2.16/1.04 Prover 6: Preprocessing ...
% 2.16/1.04 Prover 3: Preprocessing ...
% 2.16/1.04 Prover 2: Preprocessing ...
% 2.16/1.04 Prover 5: Preprocessing ...
% 2.16/1.04 Prover 0: Preprocessing ...
% 3.41/1.24 Prover 1: Warning: ignoring some quantifiers
% 3.41/1.24 Prover 5: Proving ...
% 3.41/1.25 Prover 6: Proving ...
% 3.41/1.25 Prover 1: Constructing countermodel ...
% 3.41/1.25 Prover 3: Warning: ignoring some quantifiers
% 3.41/1.26 Prover 2: Proving ...
% 3.41/1.26 Prover 3: Constructing countermodel ...
% 3.41/1.26 Prover 4: Warning: ignoring some quantifiers
% 3.41/1.27 Prover 0: Proving ...
% 3.41/1.28 Prover 4: Constructing countermodel ...
% 3.85/1.41 Prover 3: proved (777ms)
% 3.85/1.41
% 3.85/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/1.43
% 3.85/1.43 Prover 2: stopped
% 3.85/1.43 Prover 0: stopped
% 4.94/1.44 Prover 6: stopped
% 4.94/1.44 Prover 5: stopped
% 4.94/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.94/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.94/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.94/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.94/1.45 Prover 7: Preprocessing ...
% 4.94/1.46 Prover 4: Found proof (size 23)
% 4.94/1.46 Prover 10: Preprocessing ...
% 4.94/1.46 Prover 4: proved (823ms)
% 4.94/1.46 Prover 1: Found proof (size 22)
% 4.94/1.46 Prover 1: proved (832ms)
% 4.94/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.94/1.46 Prover 8: Preprocessing ...
% 4.94/1.46 Prover 7: stopped
% 4.94/1.47 Prover 11: Preprocessing ...
% 4.94/1.47 Prover 13: Preprocessing ...
% 4.94/1.48 Prover 10: stopped
% 4.94/1.49 Prover 13: stopped
% 4.94/1.50 Prover 11: stopped
% 5.49/1.54 Prover 8: Warning: ignoring some quantifiers
% 5.49/1.55 Prover 8: Constructing countermodel ...
% 5.49/1.55 Prover 8: stopped
% 5.49/1.55
% 5.49/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.49/1.55
% 5.49/1.56 % SZS output start Proof for theBenchmark
% 5.49/1.56 Assumptions after simplification:
% 5.49/1.56 ---------------------------------
% 5.49/1.56
% 5.49/1.56 (commutativity_of_intersection)
% 5.75/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~
% 5.75/1.60 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] :
% 5.75/1.60 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~
% 5.75/1.60 $i(v0) | (intersection(v1, v0) = v2 & $i(v2)))
% 5.75/1.60
% 5.75/1.60 (intersect_defn)
% 5.75/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 5.75/1.60 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) |
% 5.75/1.60 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0:
% 5.75/1.60 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0,
% 5.75/1.60 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0)
% 5.75/1.60 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : !
% 5.75/1.60 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 5.75/1.60 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 5.75/1.60
% 5.75/1.60 (intersection_defn)
% 5.75/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 5.75/1.61 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~
% 5.75/1.61 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 &
% 5.75/1.61 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 5.75/1.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~
% 5.75/1.61 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) =
% 5.75/1.61 0 & member(v2, v0) = 0))
% 5.75/1.61
% 5.75/1.61 (prove_th102)
% 5.75/1.61 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 5.75/1.61 = 0) & intersect(v0, v3) = 0 & intersect(v0, v1) = v4 & intersection(v1,
% 5.75/1.61 v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.75/1.61
% 5.75/1.61 (function-axioms)
% 5.75/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 5.75/1.61 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) =
% 5.75/1.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 5.75/1.61 ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0:
% 5.75/1.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 5.75/1.61 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 5.75/1.61
% 5.75/1.61 Further assumptions not needed in the proof:
% 5.75/1.61 --------------------------------------------
% 5.75/1.61 equal_member_defn, symmetry_of_intersect
% 5.75/1.61
% 5.75/1.61 Those formulas are unsatisfiable:
% 5.75/1.61 ---------------------------------
% 5.75/1.61
% 5.75/1.61 Begin of proof
% 5.75/1.61 |
% 5.75/1.62 | ALPHA: (intersection_defn) implies:
% 5.75/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 5.75/1.62 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) |
% 5.75/1.62 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 5.75/1.62 |
% 5.75/1.62 | ALPHA: (intersect_defn) implies:
% 5.75/1.62 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) |
% 5.75/1.62 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 &
% 5.75/1.62 | $i(v2)))
% 5.75/1.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 5.75/1.62 | (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~
% 5.75/1.62 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) =
% 5.75/1.62 | v4))
% 5.75/1.62 |
% 5.75/1.62 | ALPHA: (commutativity_of_intersection) implies:
% 5.75/1.62 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) =
% 5.75/1.62 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2)))
% 5.75/1.62 |
% 5.75/1.62 | ALPHA: (function-axioms) implies:
% 5.75/1.62 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 5.75/1.62 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 5.75/1.62 | = v0))
% 5.75/1.62 |
% 5.75/1.62 | DELTA: instantiating (prove_th102) with fresh symbols all_7_0, all_7_1,
% 5.75/1.62 | all_7_2, all_7_3, all_7_4 gives:
% 5.75/1.63 | (6) ~ (all_7_0 = 0) & intersect(all_7_4, all_7_1) = 0 & intersect(all_7_4,
% 5.75/1.63 | all_7_3) = all_7_0 & intersection(all_7_3, all_7_2) = all_7_1 &
% 5.75/1.63 | $i(all_7_1) & $i(all_7_2) & $i(all_7_3) & $i(all_7_4)
% 5.75/1.63 |
% 5.75/1.63 | ALPHA: (6) implies:
% 5.75/1.63 | (7) ~ (all_7_0 = 0)
% 5.75/1.63 | (8) $i(all_7_4)
% 5.75/1.63 | (9) $i(all_7_3)
% 5.75/1.63 | (10) $i(all_7_2)
% 5.75/1.63 | (11) intersection(all_7_3, all_7_2) = all_7_1
% 5.75/1.63 | (12) intersect(all_7_4, all_7_3) = all_7_0
% 5.75/1.63 | (13) intersect(all_7_4, all_7_1) = 0
% 5.75/1.63 |
% 5.75/1.63 | GROUND_INST: instantiating (4) with all_7_2, all_7_3, all_7_1, simplifying
% 5.75/1.63 | with (9), (10), (11) gives:
% 5.75/1.63 | (14) intersection(all_7_2, all_7_3) = all_7_1 & $i(all_7_1)
% 5.75/1.63 |
% 5.75/1.63 | ALPHA: (14) implies:
% 5.75/1.63 | (15) $i(all_7_1)
% 5.75/1.63 | (16) intersection(all_7_2, all_7_3) = all_7_1
% 5.75/1.63 |
% 5.75/1.63 | GROUND_INST: instantiating (2) with all_7_4, all_7_1, simplifying with (8),
% 5.75/1.63 | (13), (15) gives:
% 5.75/1.63 | (17) ? [v0: $i] : (member(v0, all_7_1) = 0 & member(v0, all_7_4) = 0 &
% 5.75/1.63 | $i(v0))
% 5.75/1.63 |
% 5.75/1.63 | DELTA: instantiating (17) with fresh symbol all_16_0 gives:
% 5.75/1.63 | (18) member(all_16_0, all_7_1) = 0 & member(all_16_0, all_7_4) = 0 &
% 5.75/1.63 | $i(all_16_0)
% 5.75/1.63 |
% 5.75/1.63 | ALPHA: (18) implies:
% 5.75/1.63 | (19) $i(all_16_0)
% 5.75/1.63 | (20) member(all_16_0, all_7_4) = 0
% 5.75/1.63 | (21) member(all_16_0, all_7_1) = 0
% 5.75/1.63 |
% 5.75/1.63 | GROUND_INST: instantiating (3) with all_7_4, all_7_3, all_7_0, all_16_0,
% 5.75/1.64 | simplifying with (8), (9), (12), (19), (20) gives:
% 5.75/1.64 | (22) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_16_0, all_7_3)
% 5.75/1.64 | = v0)
% 5.75/1.64 |
% 5.75/1.64 | GROUND_INST: instantiating (1) with all_7_2, all_7_3, all_16_0, all_7_1,
% 5.75/1.64 | simplifying with (9), (10), (16), (19), (21) gives:
% 5.75/1.64 | (23) member(all_16_0, all_7_2) = 0 & member(all_16_0, all_7_3) = 0
% 5.75/1.64 |
% 5.75/1.64 | ALPHA: (23) implies:
% 5.75/1.64 | (24) member(all_16_0, all_7_3) = 0
% 5.75/1.64 |
% 5.75/1.64 | BETA: splitting (22) gives:
% 5.75/1.64 |
% 5.75/1.64 | Case 1:
% 5.75/1.64 | |
% 5.75/1.64 | | (25) all_7_0 = 0
% 5.75/1.64 | |
% 5.75/1.64 | | REDUCE: (7), (25) imply:
% 5.75/1.64 | | (26) $false
% 5.75/1.64 | |
% 5.75/1.64 | | CLOSE: (26) is inconsistent.
% 5.75/1.64 | |
% 5.75/1.64 | Case 2:
% 5.75/1.64 | |
% 5.75/1.64 | | (27) ? [v0: int] : ( ~ (v0 = 0) & member(all_16_0, all_7_3) = v0)
% 5.75/1.64 | |
% 5.75/1.64 | | DELTA: instantiating (27) with fresh symbol all_36_0 gives:
% 5.75/1.64 | | (28) ~ (all_36_0 = 0) & member(all_16_0, all_7_3) = all_36_0
% 5.75/1.64 | |
% 5.75/1.64 | | ALPHA: (28) implies:
% 5.75/1.64 | | (29) ~ (all_36_0 = 0)
% 5.75/1.64 | | (30) member(all_16_0, all_7_3) = all_36_0
% 5.75/1.64 | |
% 5.75/1.64 | | GROUND_INST: instantiating (5) with 0, all_36_0, all_7_3, all_16_0,
% 5.75/1.64 | | simplifying with (24), (30) gives:
% 5.75/1.64 | | (31) all_36_0 = 0
% 5.75/1.64 | |
% 5.75/1.64 | | REDUCE: (29), (31) imply:
% 5.75/1.64 | | (32) $false
% 5.75/1.64 | |
% 5.75/1.64 | | CLOSE: (32) is inconsistent.
% 5.75/1.64 | |
% 5.75/1.64 | End of split
% 5.75/1.64 |
% 5.75/1.64 End of proof
% 5.75/1.64 % SZS output end Proof for theBenchmark
% 5.75/1.64
% 5.75/1.64 1040ms
%------------------------------------------------------------------------------