TSTP Solution File: GEO086+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO086+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 : n013.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 23:21:20 EDT 2023
% Result : Theorem 6.71s 1.63s
% Output : Proof 10.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO086+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 23:06:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.29/1.06 Prover 1: Preprocessing ...
% 2.29/1.06 Prover 4: Preprocessing ...
% 3.03/1.10 Prover 5: Preprocessing ...
% 3.03/1.10 Prover 3: Preprocessing ...
% 3.03/1.10 Prover 2: Preprocessing ...
% 3.03/1.10 Prover 6: Preprocessing ...
% 3.03/1.10 Prover 0: Preprocessing ...
% 5.91/1.51 Prover 2: Proving ...
% 5.91/1.51 Prover 5: Proving ...
% 6.32/1.55 Prover 1: Warning: ignoring some quantifiers
% 6.32/1.56 Prover 6: Proving ...
% 6.32/1.56 Prover 3: Warning: ignoring some quantifiers
% 6.32/1.59 Prover 1: Constructing countermodel ...
% 6.32/1.59 Prover 3: Constructing countermodel ...
% 6.71/1.63 Prover 2: proved (998ms)
% 6.71/1.63
% 6.71/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.71/1.63
% 6.71/1.63 Prover 5: proved (987ms)
% 6.71/1.63
% 6.71/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.71/1.63
% 6.71/1.64 Prover 6: proved (989ms)
% 6.71/1.64
% 6.71/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.71/1.64
% 6.71/1.65 Prover 3: stopped
% 7.10/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.10/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.10/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.10/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.10/1.69 Prover 7: Preprocessing ...
% 7.10/1.70 Prover 8: Preprocessing ...
% 7.10/1.70 Prover 10: Preprocessing ...
% 7.69/1.77 Prover 11: Preprocessing ...
% 8.04/1.79 Prover 1: Found proof (size 12)
% 8.04/1.79 Prover 1: proved (1161ms)
% 8.04/1.80 Prover 7: Warning: ignoring some quantifiers
% 8.04/1.81 Prover 10: Warning: ignoring some quantifiers
% 8.04/1.82 Prover 7: Constructing countermodel ...
% 8.04/1.83 Prover 7: stopped
% 8.04/1.84 Prover 10: Constructing countermodel ...
% 8.42/1.84 Prover 11: stopped
% 8.42/1.85 Prover 10: stopped
% 8.42/1.86 Prover 8: Warning: ignoring some quantifiers
% 8.42/1.88 Prover 8: Constructing countermodel ...
% 8.42/1.89 Prover 8: stopped
% 9.18/1.97 Prover 4: Warning: ignoring some quantifiers
% 9.48/2.02 Prover 4: Constructing countermodel ...
% 9.48/2.03 Prover 4: stopped
% 9.67/2.07 Prover 0: Proving ...
% 9.67/2.08 Prover 0: stopped
% 9.67/2.08
% 9.67/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.67/2.08
% 9.67/2.08 % SZS output start Proof for theBenchmark
% 9.67/2.08 Assumptions after simplification:
% 9.67/2.08 ---------------------------------
% 9.67/2.08
% 9.67/2.08 (c1)
% 9.67/2.11 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (part_of(v1, v0) = 0) | ~ $i(v1) |
% 9.67/2.11 ~ $i(v0) | open(v1) = 0)
% 9.67/2.11
% 9.67/2.11 (theorem_2_7_2)
% 9.67/2.11 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & open(v1) = v2 &
% 9.67/2.11 open(v0) = 0 & part_of(v1, v0) = 0 & $i(v1) & $i(v0))
% 9.67/2.11
% 9.67/2.11 (function-axioms)
% 9.67/2.12 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.67/2.12 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4,
% 9.67/2.12 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 9.67/2.12 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 9.67/2.12 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.67/2.12 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 9.67/2.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 9.67/2.12 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.67/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 9.67/2.12 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.67/2.12 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.67/2.12 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 9.67/2.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.67/2.12 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.67/2.12 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 9.67/2.12 (closed(v2) = v0))
% 9.67/2.12
% 9.67/2.12 Further assumptions not needed in the proof:
% 9.67/2.12 --------------------------------------------
% 9.67/2.12 c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn, inner_point_defn,
% 9.67/2.12 meet_defn, open_defn, part_of_defn, sum_defn
% 9.67/2.12
% 9.67/2.12 Those formulas are unsatisfiable:
% 9.67/2.12 ---------------------------------
% 9.67/2.12
% 9.67/2.12 Begin of proof
% 9.67/2.12 |
% 9.67/2.12 | ALPHA: (function-axioms) implies:
% 9.67/2.12 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.67/2.12 | (v1 = v0 | ~ (open(v2) = v1) | ~ (open(v2) = v0))
% 9.67/2.12 |
% 9.67/2.12 | DELTA: instantiating (theorem_2_7_2) with fresh symbols all_18_0, all_18_1,
% 9.67/2.12 | all_18_2 gives:
% 9.67/2.13 | (2) ~ (all_18_0 = 0) & open(all_18_1) = all_18_0 & open(all_18_2) = 0 &
% 9.67/2.13 | part_of(all_18_1, all_18_2) = 0 & $i(all_18_1) & $i(all_18_2)
% 9.67/2.13 |
% 9.67/2.13 | ALPHA: (2) implies:
% 9.67/2.13 | (3) ~ (all_18_0 = 0)
% 9.67/2.13 | (4) $i(all_18_2)
% 9.67/2.13 | (5) $i(all_18_1)
% 9.67/2.13 | (6) part_of(all_18_1, all_18_2) = 0
% 9.67/2.13 | (7) open(all_18_2) = 0
% 9.67/2.13 | (8) open(all_18_1) = all_18_0
% 9.67/2.13 |
% 9.67/2.13 | GROUND_INST: instantiating (c1) with all_18_2, all_18_1, simplifying with (4),
% 9.67/2.13 | (5), (6) gives:
% 9.67/2.13 | (9) all_18_1 = all_18_2 | open(all_18_1) = 0
% 9.67/2.13 |
% 9.67/2.13 | BETA: splitting (9) gives:
% 9.67/2.13 |
% 9.67/2.13 | Case 1:
% 9.67/2.13 | |
% 9.67/2.13 | | (10) open(all_18_1) = 0
% 9.67/2.13 | |
% 9.67/2.13 | | GROUND_INST: instantiating (1) with all_18_0, 0, all_18_1, simplifying with
% 9.67/2.13 | | (8), (10) gives:
% 9.67/2.13 | | (11) all_18_0 = 0
% 9.67/2.13 | |
% 9.67/2.13 | | REDUCE: (3), (11) imply:
% 9.67/2.13 | | (12) $false
% 9.67/2.13 | |
% 9.67/2.13 | | CLOSE: (12) is inconsistent.
% 9.67/2.13 | |
% 9.67/2.13 | Case 2:
% 9.67/2.13 | |
% 9.67/2.13 | | (13) all_18_1 = all_18_2
% 9.67/2.13 | | (14) ~ (open(all_18_1) = 0)
% 10.09/2.13 | |
% 10.09/2.13 | | REDUCE: (13), (14) imply:
% 10.09/2.13 | | (15) ~ (open(all_18_2) = 0)
% 10.09/2.13 | |
% 10.09/2.13 | | PRED_UNIFY: (7), (15) imply:
% 10.09/2.13 | | (16) $false
% 10.09/2.13 | |
% 10.09/2.13 | | CLOSE: (16) is inconsistent.
% 10.09/2.13 | |
% 10.09/2.13 | End of split
% 10.09/2.13 |
% 10.09/2.13 End of proof
% 10.09/2.13 % SZS output end Proof for theBenchmark
% 10.09/2.13
% 10.09/2.13 1522ms
%------------------------------------------------------------------------------