TSTP Solution File: GEO117+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO117+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 : n015.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 23:21:30 EDT 2023
% Result : Theorem 11.58s 2.60s
% Output : Proof 18.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n015.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 23:41:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.70 ________ _____
% 0.20/0.70 ___ __ \_________(_)________________________________
% 0.20/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.70
% 0.20/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.70 (2023-06-19)
% 0.20/0.70
% 0.20/0.70 (c) Philipp Rümmer, 2009-2023
% 0.20/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.70 Amanda Stjerna.
% 0.20/0.70 Free software under BSD-3-Clause.
% 0.20/0.70
% 0.20/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.70
% 0.20/0.70 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.72 Running up to 7 provers in parallel.
% 0.20/0.75 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.75 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.75 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.75 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.75 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.88/1.40 Prover 1: Preprocessing ...
% 3.88/1.40 Prover 4: Preprocessing ...
% 3.88/1.46 Prover 6: Preprocessing ...
% 3.88/1.46 Prover 5: Preprocessing ...
% 3.88/1.46 Prover 0: Preprocessing ...
% 3.88/1.46 Prover 2: Preprocessing ...
% 3.88/1.46 Prover 3: Preprocessing ...
% 8.16/2.19 Prover 5: Proving ...
% 8.16/2.24 Prover 2: Proving ...
% 8.16/2.30 Prover 1: Warning: ignoring some quantifiers
% 9.47/2.34 Prover 6: Proving ...
% 10.32/2.42 Prover 3: Warning: ignoring some quantifiers
% 10.67/2.48 Prover 3: Constructing countermodel ...
% 10.67/2.48 Prover 1: Constructing countermodel ...
% 11.58/2.60 Prover 2: proved (1871ms)
% 11.58/2.60
% 11.58/2.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.58/2.60
% 11.58/2.61 Prover 3: stopped
% 11.58/2.63 Prover 6: stopped
% 11.58/2.63 Prover 5: stopped
% 11.92/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.92/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.92/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.04/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.04/2.70 Prover 7: Preprocessing ...
% 12.04/2.71 Prover 8: Preprocessing ...
% 12.52/2.72 Prover 11: Preprocessing ...
% 12.52/2.74 Prover 10: Preprocessing ...
% 13.48/2.95 Prover 7: Warning: ignoring some quantifiers
% 13.48/3.00 Prover 10: Warning: ignoring some quantifiers
% 13.48/3.01 Prover 7: Constructing countermodel ...
% 13.48/3.05 Prover 10: Constructing countermodel ...
% 15.54/3.15 Prover 8: Warning: ignoring some quantifiers
% 15.54/3.18 Prover 8: Constructing countermodel ...
% 15.54/3.21 Prover 4: Warning: ignoring some quantifiers
% 16.19/3.22 Prover 7: Found proof (size 11)
% 16.19/3.22 Prover 10: Found proof (size 11)
% 16.19/3.22 Prover 7: proved (610ms)
% 16.19/3.22 Prover 10: proved (583ms)
% 16.19/3.22 Prover 8: stopped
% 16.19/3.22 Prover 1: stopped
% 16.19/3.28 Prover 4: Constructing countermodel ...
% 16.61/3.29 Prover 4: stopped
% 17.15/3.38 Prover 0: Proving ...
% 17.15/3.40 Prover 0: stopped
% 17.78/3.54 Prover 11: Warning: ignoring some quantifiers
% 17.78/3.58 Prover 11: Constructing countermodel ...
% 18.07/3.60 Prover 11: stopped
% 18.07/3.60
% 18.07/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.07/3.60
% 18.07/3.61 % SZS output start Proof for theBenchmark
% 18.07/3.61 Assumptions after simplification:
% 18.07/3.61 ---------------------------------
% 18.07/3.61
% 18.07/3.61 (between_c_defn)
% 18.07/3.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 18.07/3.62 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.07/3.62 inner_point(v2, v4) | ~ end_point(v3, v4) | ~ end_point(v1, v4) | ~
% 18.07/3.62 part_of(v4, v0) | between_c(v0, v1, v2, v3)) & ! [v0: $i] : ! [v1: $i] :
% 18.07/3.62 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.07/3.62 between_c(v0, v1, v2, v3) | ? [v4: $i] : ($i(v4) & inner_point(v2, v4) &
% 18.07/3.62 end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) & ! [v0: $i] :
% 18.07/3.62 ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.07/3.62 between_c(v0, v1, v2, v1))
% 18.07/3.62
% 18.07/3.62 (between_o_defn)
% 18.07/3.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 18.07/3.63 | ~ $i(v1) | ~ $i(v0) | ~ ordered_by(v0, v3, v2) | ~ ordered_by(v0, v2,
% 18.07/3.63 v1) | between_o(v0, v1, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 18.07/3.63 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 18.07/3.63 ordered_by(v0, v2, v3) | ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2,
% 18.07/3.63 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 18.07/3.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v0, v1, v2, v3) |
% 18.07/3.63 ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i]
% 18.07/3.63 : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.07/3.63 ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1,
% 18.07/3.63 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 18.07/3.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v0, v1, v2, v3) |
% 18.07/3.63 ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 18.07/3.63 : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 18.07/3.63 ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1,
% 18.07/3.63 v2))
% 18.07/3.63
% 18.07/3.63 (o3)
% 18.07/3.64 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 18.07/3.64 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_c(v4,
% 18.07/3.64 v1, v2, v3) | between_o(v0, v1, v2, v3) | ? [v5: $i] : ($i(v5) & ( ~
% 18.07/3.64 incident_o(v5, v0) | ~ incident_c(v5, v4)) & (incident_o(v5, v0) |
% 18.07/3.64 incident_c(v5, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.07/3.64 [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v3,
% 18.07/3.64 v0, v1, v2) | ? [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) & ! [v5:
% 18.07/3.64 $i] : ( ~ $i(v5) | ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5:
% 18.07/3.64 $i] : ( ~ $i(v5) | ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 18.07/3.64
% 18.07/3.64 (theorem_4_4)
% 18.07/3.64 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ordered_by(v0, v1, v1))
% 18.07/3.64
% 18.07/3.64 Further assumptions not needed in the proof:
% 18.07/3.64 --------------------------------------------
% 18.07/3.64 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 18.07/3.64 finish_point_defn, inner_point_defn, meet_defn, o1, o2, o4, o5, o6, open_defn,
% 18.07/3.64 part_of_defn, start_point_defn, sum_defn, underlying_curve_defn
% 18.07/3.64
% 18.07/3.64 Those formulas are unsatisfiable:
% 18.07/3.64 ---------------------------------
% 18.07/3.64
% 18.07/3.64 Begin of proof
% 18.07/3.64 |
% 18.07/3.64 | ALPHA: (between_c_defn) implies:
% 18.07/3.64 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 18.07/3.64 | $i(v0) | ~ between_c(v0, v1, v2, v1))
% 18.07/3.64 |
% 18.07/3.64 | ALPHA: (between_o_defn) implies:
% 18.07/3.64 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 18.07/3.64 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ordered_by(v0, v3, v2) | ~
% 18.07/3.64 | ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3))
% 18.07/3.64 |
% 18.07/3.64 | ALPHA: (o3) implies:
% 18.07/3.64 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 18.07/3.64 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v3, v0, v1, v2) | ?
% 18.07/3.64 | [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) & ! [v5: $i] : ( ~
% 18.07/3.64 | $i(v5) | ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5:
% 18.07/3.64 | $i] : ( ~ $i(v5) | ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 18.07/3.64 |
% 18.07/3.64 | DELTA: instantiating (theorem_4_4) with fresh symbols all_25_0, all_25_1
% 18.07/3.64 | gives:
% 18.07/3.65 | (4) $i(all_25_0) & $i(all_25_1) & ordered_by(all_25_1, all_25_0, all_25_0)
% 18.07/3.65 |
% 18.07/3.65 | ALPHA: (4) implies:
% 18.07/3.65 | (5) ordered_by(all_25_1, all_25_0, all_25_0)
% 18.07/3.65 | (6) $i(all_25_1)
% 18.07/3.65 | (7) $i(all_25_0)
% 18.07/3.65 |
% 18.07/3.65 | GROUND_INST: instantiating (2) with all_25_1, all_25_0, all_25_0, all_25_0,
% 18.07/3.65 | simplifying with (5), (6), (7) gives:
% 18.07/3.65 | (8) between_o(all_25_1, all_25_0, all_25_0, all_25_0)
% 18.07/3.65 |
% 18.07/3.65 | GROUND_INST: instantiating (3) with all_25_0, all_25_0, all_25_0, all_25_1,
% 18.07/3.65 | simplifying with (6), (7), (8) gives:
% 18.07/3.65 | (9) ? [v0: $i] : ($i(v0) & between_c(v0, all_25_0, all_25_0, all_25_0) &
% 18.07/3.65 | ! [v1: $i] : ( ~ $i(v1) | ~ incident_o(v1, all_25_1) |
% 18.07/3.65 | incident_c(v1, v0)) & ! [v1: $i] : ( ~ $i(v1) | ~ incident_c(v1,
% 18.07/3.65 | v0) | incident_o(v1, all_25_1)))
% 18.07/3.65 |
% 18.07/3.65 | DELTA: instantiating (9) with fresh symbol all_51_0 gives:
% 18.07/3.65 | (10) $i(all_51_0) & between_c(all_51_0, all_25_0, all_25_0, all_25_0) & !
% 18.07/3.65 | [v0: $i] : ( ~ $i(v0) | ~ incident_o(v0, all_25_1) | incident_c(v0,
% 18.07/3.65 | all_51_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ incident_c(v0,
% 18.07/3.65 | all_51_0) | incident_o(v0, all_25_1))
% 18.07/3.65 |
% 18.07/3.65 | ALPHA: (10) implies:
% 18.07/3.65 | (11) between_c(all_51_0, all_25_0, all_25_0, all_25_0)
% 18.07/3.65 | (12) $i(all_51_0)
% 18.07/3.65 |
% 18.07/3.65 | GROUND_INST: instantiating (1) with all_51_0, all_25_0, all_25_0, simplifying
% 18.07/3.65 | with (7), (11), (12) gives:
% 18.07/3.65 | (13) $false
% 18.07/3.66 |
% 18.07/3.66 | CLOSE: (13) is inconsistent.
% 18.07/3.66 |
% 18.07/3.66 End of proof
% 18.07/3.66 % SZS output end Proof for theBenchmark
% 18.07/3.66
% 18.07/3.66 2951ms
%------------------------------------------------------------------------------