TSTP Solution File: GEO081+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO081+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 : Wed Aug 30 23:21:18 EDT 2023
% Result : Theorem 6.52s 2.83s
% Output : Proof 9.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.20 % Problem : GEO081+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.21 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.44 % Computer : n008.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Tue Aug 29 20:48:32 EDT 2023
% 0.13/0.44 % CPUTime :
% 0.16/0.78 ________ _____
% 0.16/0.78 ___ __ \_________(_)________________________________
% 0.16/0.78 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.78 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.78 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.78
% 0.16/0.78 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.78 (2023-06-19)
% 0.16/0.78
% 0.16/0.78 (c) Philipp Rümmer, 2009-2023
% 0.16/0.78 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.78 Amanda Stjerna.
% 0.16/0.78 Free software under BSD-3-Clause.
% 0.16/0.78
% 0.16/0.78 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.78
% 0.16/0.78 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.80 Running up to 7 provers in parallel.
% 0.66/0.89 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.89 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.89 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.89 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.89 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.89 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.41/1.47 Prover 1: Preprocessing ...
% 1.41/1.49 Prover 4: Preprocessing ...
% 2.06/1.57 Prover 6: Preprocessing ...
% 2.06/1.57 Prover 3: Preprocessing ...
% 2.06/1.57 Prover 2: Preprocessing ...
% 2.06/1.57 Prover 5: Preprocessing ...
% 2.06/1.57 Prover 0: Preprocessing ...
% 4.33/2.36 Prover 5: Proving ...
% 4.71/2.40 Prover 2: Proving ...
% 5.10/2.45 Prover 1: Warning: ignoring some quantifiers
% 5.10/2.47 Prover 3: Warning: ignoring some quantifiers
% 5.10/2.47 Prover 6: Proving ...
% 5.44/2.52 Prover 3: Constructing countermodel ...
% 5.44/2.53 Prover 1: Constructing countermodel ...
% 6.52/2.83 Prover 3: proved (1977ms)
% 6.52/2.83
% 6.52/2.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.52/2.83
% 6.52/2.86 Prover 2: stopped
% 6.52/2.87 Prover 6: stopped
% 6.52/2.88 Prover 5: stopped
% 6.77/2.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.77/2.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.77/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.77/2.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.77/3.04 Prover 8: Preprocessing ...
% 6.77/3.06 Prover 11: Preprocessing ...
% 6.77/3.06 Prover 7: Preprocessing ...
% 6.77/3.07 Prover 10: Preprocessing ...
% 6.77/3.12 Prover 1: Found proof (size 29)
% 6.77/3.12 Prover 1: proved (2284ms)
% 6.77/3.12 Prover 10: stopped
% 6.77/3.20 Prover 7: Warning: ignoring some quantifiers
% 6.77/3.24 Prover 7: Constructing countermodel ...
% 6.77/3.24 Prover 11: stopped
% 6.77/3.25 Prover 7: stopped
% 8.37/3.31 Prover 8: Warning: ignoring some quantifiers
% 8.42/3.34 Prover 8: Constructing countermodel ...
% 8.42/3.35 Prover 8: stopped
% 8.74/3.45 Prover 4: Warning: ignoring some quantifiers
% 9.01/3.55 Prover 4: Constructing countermodel ...
% 9.01/3.57 Prover 4: stopped
% 9.42/3.64 Prover 0: Proving ...
% 9.42/3.67 Prover 0: stopped
% 9.42/3.67
% 9.42/3.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.42/3.67
% 9.42/3.67 % SZS output start Proof for theBenchmark
% 9.42/3.68 Assumptions after simplification:
% 9.42/3.68 ---------------------------------
% 9.42/3.68
% 9.42/3.68 (part_of_defn)
% 9.63/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2)
% 9.63/3.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 9.63/3.75 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i]
% 9.63/3.75 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2:
% 9.63/3.75 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) |
% 9.63/3.75 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)))
% 9.63/3.75
% 9.63/3.75 (part_of_transitivity)
% 9.63/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.63/3.75 part_of(v1, v2) = 0 & part_of(v0, v2) = v3 & part_of(v0, v1) = 0 & $i(v2) &
% 9.63/3.75 $i(v1) & $i(v0))
% 9.63/3.75
% 9.63/3.75 (function-axioms)
% 9.63/3.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.63/3.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4,
% 9.63/3.76 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 9.63/3.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 9.63/3.76 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.63/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.63/3.76 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 9.63/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 9.63/3.76 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.63/3.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 9.63/3.76 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.63/3.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.63/3.76 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 9.63/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.63/3.76 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.63/3.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 9.63/3.76 (closed(v2) = v0))
% 9.63/3.76
% 9.63/3.76 Further assumptions not needed in the proof:
% 9.63/3.76 --------------------------------------------
% 9.63/3.76 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 9.63/3.76 inner_point_defn, meet_defn, open_defn, sum_defn
% 9.63/3.76
% 9.63/3.76 Those formulas are unsatisfiable:
% 9.63/3.76 ---------------------------------
% 9.63/3.76
% 9.63/3.76 Begin of proof
% 9.63/3.76 |
% 9.63/3.76 | ALPHA: (part_of_defn) implies:
% 9.63/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~
% 9.63/3.77 | $i(v0) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2,
% 9.63/3.77 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 9.63/3.77 | incident_c(v2, v1) = v4)))
% 9.63/3.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1,
% 9.63/3.77 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 9.63/3.77 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 &
% 9.63/3.77 | $i(v3)))
% 9.63/3.77 |
% 9.63/3.77 | ALPHA: (function-axioms) implies:
% 9.63/3.77 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.63/3.77 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~
% 9.63/3.77 | (incident_c(v3, v2) = v0))
% 9.63/3.77 |
% 9.63/3.77 | DELTA: instantiating (part_of_transitivity) with fresh symbols all_18_0,
% 9.63/3.77 | all_18_1, all_18_2, all_18_3 gives:
% 9.63/3.78 | (4) ~ (all_18_0 = 0) & part_of(all_18_2, all_18_1) = 0 & part_of(all_18_3,
% 9.63/3.78 | all_18_1) = all_18_0 & part_of(all_18_3, all_18_2) = 0 & $i(all_18_1)
% 9.63/3.78 | & $i(all_18_2) & $i(all_18_3)
% 9.63/3.78 |
% 9.63/3.78 | ALPHA: (4) implies:
% 9.63/3.78 | (5) ~ (all_18_0 = 0)
% 9.63/3.78 | (6) $i(all_18_3)
% 9.63/3.78 | (7) $i(all_18_2)
% 9.63/3.78 | (8) $i(all_18_1)
% 9.63/3.78 | (9) part_of(all_18_3, all_18_2) = 0
% 9.63/3.78 | (10) part_of(all_18_3, all_18_1) = all_18_0
% 9.63/3.78 | (11) part_of(all_18_2, all_18_1) = 0
% 9.63/3.78 |
% 9.63/3.78 | GROUND_INST: instantiating (1) with all_18_2, all_18_3, simplifying with (6),
% 9.63/3.78 | (7), (9) gives:
% 9.63/3.79 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_18_2) =
% 9.63/3.79 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 9.63/3.79 | all_18_3) = v2))
% 9.63/3.79 |
% 9.63/3.79 | GROUND_INST: instantiating (2) with all_18_1, all_18_3, all_18_0, simplifying
% 9.63/3.79 | with (6), (8), (10) gives:
% 9.63/3.80 | (13) all_18_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.63/3.80 | incident_c(v0, all_18_1) = v1 & incident_c(v0, all_18_3) = 0 &
% 9.63/3.80 | $i(v0))
% 9.63/3.80 |
% 9.63/3.80 | GROUND_INST: instantiating (1) with all_18_1, all_18_2, simplifying with (7),
% 9.63/3.80 | (8), (11) gives:
% 9.63/3.80 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_18_1) =
% 9.63/3.80 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 9.63/3.80 | all_18_2) = v2))
% 9.63/3.80 |
% 9.63/3.80 | BETA: splitting (13) gives:
% 9.63/3.80 |
% 9.63/3.80 | Case 1:
% 9.63/3.80 | |
% 9.63/3.80 | | (15) all_18_0 = 0
% 9.63/3.80 | |
% 9.63/3.80 | | REDUCE: (5), (15) imply:
% 9.63/3.80 | | (16) $false
% 9.63/3.80 | |
% 9.63/3.80 | | CLOSE: (16) is inconsistent.
% 9.63/3.80 | |
% 9.63/3.80 | Case 2:
% 9.63/3.80 | |
% 9.63/3.80 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_18_1)
% 9.63/3.80 | | = v1 & incident_c(v0, all_18_3) = 0 & $i(v0))
% 9.63/3.80 | |
% 9.63/3.80 | | DELTA: instantiating (17) with fresh symbols all_33_0, all_33_1 gives:
% 9.63/3.80 | | (18) ~ (all_33_0 = 0) & incident_c(all_33_1, all_18_1) = all_33_0 &
% 9.63/3.80 | | incident_c(all_33_1, all_18_3) = 0 & $i(all_33_1)
% 9.63/3.80 | |
% 9.63/3.80 | | ALPHA: (18) implies:
% 9.63/3.80 | | (19) ~ (all_33_0 = 0)
% 9.63/3.81 | | (20) $i(all_33_1)
% 9.63/3.81 | | (21) incident_c(all_33_1, all_18_3) = 0
% 9.63/3.81 | | (22) incident_c(all_33_1, all_18_1) = all_33_0
% 9.63/3.81 | |
% 9.63/3.81 | | GROUND_INST: instantiating (14) with all_33_1, all_33_0, simplifying with
% 9.63/3.81 | | (20), (22) gives:
% 9.63/3.81 | | (23) all_33_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1,
% 9.63/3.81 | | all_18_2) = v0)
% 9.63/3.81 | |
% 9.63/3.81 | | BETA: splitting (23) gives:
% 9.63/3.81 | |
% 9.63/3.81 | | Case 1:
% 9.63/3.81 | | |
% 9.63/3.81 | | | (24) all_33_0 = 0
% 9.63/3.81 | | |
% 9.63/3.81 | | | REDUCE: (19), (24) imply:
% 9.63/3.81 | | | (25) $false
% 9.63/3.81 | | |
% 9.63/3.81 | | | CLOSE: (25) is inconsistent.
% 9.63/3.81 | | |
% 9.63/3.81 | | Case 2:
% 9.63/3.81 | | |
% 9.63/3.81 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, all_18_2) = v0)
% 9.63/3.81 | | |
% 9.63/3.81 | | | DELTA: instantiating (26) with fresh symbol all_46_0 gives:
% 9.63/3.81 | | | (27) ~ (all_46_0 = 0) & incident_c(all_33_1, all_18_2) = all_46_0
% 9.63/3.81 | | |
% 9.63/3.81 | | | ALPHA: (27) implies:
% 9.63/3.81 | | | (28) ~ (all_46_0 = 0)
% 9.63/3.84 | | | (29) incident_c(all_33_1, all_18_2) = all_46_0
% 9.63/3.84 | | |
% 9.63/3.84 | | | GROUND_INST: instantiating (12) with all_33_1, all_46_0, simplifying with
% 9.63/3.84 | | | (20), (29) gives:
% 9.63/3.84 | | | (30) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1,
% 9.63/3.84 | | | all_18_3) = v0)
% 9.63/3.84 | | |
% 9.63/3.84 | | | BETA: splitting (30) gives:
% 9.63/3.84 | | |
% 9.63/3.84 | | | Case 1:
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | (31) all_46_0 = 0
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | REDUCE: (28), (31) imply:
% 9.63/3.84 | | | | (32) $false
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | CLOSE: (32) is inconsistent.
% 9.63/3.84 | | | |
% 9.63/3.84 | | | Case 2:
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | (33) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_33_1, all_18_3) =
% 9.63/3.84 | | | | v0)
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | DELTA: instantiating (33) with fresh symbol all_59_0 gives:
% 9.63/3.84 | | | | (34) ~ (all_59_0 = 0) & incident_c(all_33_1, all_18_3) = all_59_0
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | ALPHA: (34) implies:
% 9.63/3.84 | | | | (35) ~ (all_59_0 = 0)
% 9.63/3.84 | | | | (36) incident_c(all_33_1, all_18_3) = all_59_0
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | GROUND_INST: instantiating (3) with 0, all_59_0, all_18_3, all_33_1,
% 9.63/3.84 | | | | simplifying with (21), (36) gives:
% 9.63/3.84 | | | | (37) all_59_0 = 0
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | REDUCE: (35), (37) imply:
% 9.63/3.84 | | | | (38) $false
% 9.63/3.84 | | | |
% 9.63/3.84 | | | | CLOSE: (38) is inconsistent.
% 9.63/3.84 | | | |
% 9.63/3.84 | | | End of split
% 9.63/3.84 | | |
% 9.63/3.84 | | End of split
% 9.63/3.84 | |
% 9.63/3.84 | End of split
% 9.63/3.84 |
% 9.63/3.84 End of proof
% 9.63/3.84 % SZS output end Proof for theBenchmark
% 9.63/3.84
% 9.63/3.84 3061ms
%------------------------------------------------------------------------------