TSTP Solution File: GEO080+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO080+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 : n002.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 8.43s 1.88s
% Output : Proof 12.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO080+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 23:00:50 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.58 ________ _____
% 0.16/0.58 ___ __ \_________(_)________________________________
% 0.16/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.58
% 0.16/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.58 (2023-06-19)
% 0.16/0.58
% 0.16/0.59 (c) Philipp Rümmer, 2009-2023
% 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.59 Amanda Stjerna.
% 0.16/0.59 Free software under BSD-3-Clause.
% 0.16/0.59
% 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.59
% 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/0.60 Running up to 7 provers in parallel.
% 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.33/1.09 Prover 1: Preprocessing ...
% 2.33/1.10 Prover 4: Preprocessing ...
% 2.98/1.13 Prover 6: Preprocessing ...
% 2.98/1.13 Prover 3: Preprocessing ...
% 2.98/1.13 Prover 2: Preprocessing ...
% 2.98/1.13 Prover 0: Preprocessing ...
% 2.98/1.13 Prover 5: Preprocessing ...
% 6.98/1.71 Prover 5: Proving ...
% 7.23/1.72 Prover 2: Proving ...
% 7.35/1.75 Prover 6: Proving ...
% 7.35/1.76 Prover 3: Warning: ignoring some quantifiers
% 7.35/1.79 Prover 1: Warning: ignoring some quantifiers
% 7.35/1.80 Prover 3: Constructing countermodel ...
% 7.96/1.82 Prover 1: Constructing countermodel ...
% 8.43/1.88 Prover 3: proved (1253ms)
% 8.43/1.88
% 8.43/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.43/1.88
% 8.43/1.88 Prover 5: stopped
% 8.43/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.43/1.89 Prover 6: stopped
% 8.43/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.43/1.91 Prover 2: stopped
% 8.43/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.43/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.43/1.96 Prover 7: Preprocessing ...
% 8.43/2.00 Prover 10: Preprocessing ...
% 8.43/2.01 Prover 8: Preprocessing ...
% 8.43/2.01 Prover 1: Found proof (size 14)
% 8.43/2.01 Prover 1: proved (1401ms)
% 8.43/2.03 Prover 10: stopped
% 8.43/2.04 Prover 11: Preprocessing ...
% 8.43/2.05 Prover 7: stopped
% 10.31/2.14 Prover 11: stopped
% 10.31/2.19 Prover 8: Warning: ignoring some quantifiers
% 10.96/2.25 Prover 8: Constructing countermodel ...
% 10.96/2.26 Prover 8: stopped
% 11.38/2.34 Prover 4: Warning: ignoring some quantifiers
% 11.72/2.41 Prover 4: Constructing countermodel ...
% 11.72/2.43 Prover 4: stopped
% 12.41/2.50 Prover 0: Proving ...
% 12.41/2.52 Prover 0: stopped
% 12.41/2.52
% 12.41/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.41/2.52
% 12.41/2.52 % SZS output start Proof for theBenchmark
% 12.41/2.53 Assumptions after simplification:
% 12.41/2.53 ---------------------------------
% 12.41/2.53
% 12.41/2.53 (part_of_defn)
% 12.65/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2)
% 12.65/2.56 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 12.65/2.56 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i]
% 12.65/2.56 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2:
% 12.65/2.56 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) |
% 12.65/2.56 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)))
% 12.65/2.56
% 12.65/2.56 (prove_reflexivity)
% 12.65/2.57 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & part_of(v0, v0) = v1 & $i(v0))
% 12.65/2.57
% 12.65/2.57 (function-axioms)
% 12.65/2.57 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.65/2.57 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4,
% 12.65/2.57 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 12.65/2.57 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 12.65/2.57 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.65/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.65/2.57 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 12.65/2.57 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 12.65/2.57 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.65/2.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 12.65/2.57 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.65/2.58 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.65/2.58 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 12.65/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.65/2.58 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.65/2.58 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 12.65/2.58 (closed(v2) = v0))
% 12.65/2.58
% 12.65/2.58 Further assumptions not needed in the proof:
% 12.65/2.58 --------------------------------------------
% 12.65/2.58 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 12.65/2.58 inner_point_defn, meet_defn, open_defn, sum_defn
% 12.65/2.58
% 12.65/2.58 Those formulas are unsatisfiable:
% 12.65/2.58 ---------------------------------
% 12.65/2.58
% 12.65/2.58 Begin of proof
% 12.65/2.58 |
% 12.65/2.58 | ALPHA: (part_of_defn) implies:
% 12.65/2.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1,
% 12.65/2.58 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 12.65/2.58 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 &
% 12.65/2.58 | $i(v3)))
% 12.65/2.58 |
% 12.65/2.58 | ALPHA: (function-axioms) implies:
% 12.65/2.58 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.65/2.58 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~
% 12.65/2.58 | (incident_c(v3, v2) = v0))
% 12.65/2.58 |
% 12.65/2.58 | DELTA: instantiating (prove_reflexivity) with fresh symbols all_17_0, all_17_1
% 12.65/2.58 | gives:
% 12.65/2.58 | (3) ~ (all_17_0 = 0) & part_of(all_17_1, all_17_1) = all_17_0 &
% 12.65/2.58 | $i(all_17_1)
% 12.65/2.58 |
% 12.65/2.59 | ALPHA: (3) implies:
% 12.65/2.59 | (4) ~ (all_17_0 = 0)
% 12.65/2.59 | (5) $i(all_17_1)
% 12.65/2.59 | (6) part_of(all_17_1, all_17_1) = all_17_0
% 12.65/2.59 |
% 12.65/2.59 | GROUND_INST: instantiating (1) with all_17_1, all_17_1, all_17_0, simplifying
% 12.65/2.59 | with (5), (6) gives:
% 12.65/2.59 | (7) all_17_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.65/2.59 | incident_c(v0, all_17_1) = v1 & incident_c(v0, all_17_1) = 0 &
% 12.65/2.59 | $i(v0))
% 12.65/2.59 |
% 12.65/2.59 | BETA: splitting (7) gives:
% 12.65/2.59 |
% 12.65/2.59 | Case 1:
% 12.65/2.59 | |
% 12.65/2.59 | | (8) all_17_0 = 0
% 12.65/2.59 | |
% 12.65/2.59 | | REDUCE: (4), (8) imply:
% 12.65/2.59 | | (9) $false
% 12.65/2.59 | |
% 12.65/2.59 | | CLOSE: (9) is inconsistent.
% 12.65/2.59 | |
% 12.65/2.59 | Case 2:
% 12.65/2.59 | |
% 12.65/2.59 | | (10) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_17_1)
% 12.65/2.59 | | = v1 & incident_c(v0, all_17_1) = 0 & $i(v0))
% 12.65/2.59 | |
% 12.65/2.59 | | DELTA: instantiating (10) with fresh symbols all_36_0, all_36_1 gives:
% 12.65/2.60 | | (11) ~ (all_36_0 = 0) & incident_c(all_36_1, all_17_1) = all_36_0 &
% 12.65/2.60 | | incident_c(all_36_1, all_17_1) = 0 & $i(all_36_1)
% 12.65/2.60 | |
% 12.65/2.60 | | ALPHA: (11) implies:
% 12.65/2.60 | | (12) ~ (all_36_0 = 0)
% 12.65/2.60 | | (13) incident_c(all_36_1, all_17_1) = 0
% 12.65/2.60 | | (14) incident_c(all_36_1, all_17_1) = all_36_0
% 12.65/2.60 | |
% 12.65/2.60 | | GROUND_INST: instantiating (2) with 0, all_36_0, all_17_1, all_36_1,
% 12.65/2.60 | | simplifying with (13), (14) gives:
% 12.65/2.60 | | (15) all_36_0 = 0
% 12.65/2.60 | |
% 12.65/2.60 | | REDUCE: (12), (15) imply:
% 12.65/2.60 | | (16) $false
% 12.65/2.60 | |
% 12.65/2.60 | | CLOSE: (16) is inconsistent.
% 12.65/2.60 | |
% 12.65/2.60 | End of split
% 12.65/2.60 |
% 12.65/2.60 End of proof
% 12.65/2.60 % SZS output end Proof for theBenchmark
% 12.65/2.60
% 12.65/2.60 2013ms
%------------------------------------------------------------------------------