TSTP Solution File: GEO118+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO118+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 : n011.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 23:21:31 EDT 2023
% Result : Theorem 9.88s 2.08s
% Output : Proof 14.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 21:13:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.39/1.19 Prover 1: Preprocessing ...
% 3.39/1.19 Prover 4: Preprocessing ...
% 3.80/1.23 Prover 0: Preprocessing ...
% 3.80/1.23 Prover 5: Preprocessing ...
% 3.80/1.23 Prover 2: Preprocessing ...
% 3.80/1.24 Prover 6: Preprocessing ...
% 3.80/1.24 Prover 3: Preprocessing ...
% 7.04/1.68 Prover 5: Proving ...
% 7.04/1.68 Prover 2: Proving ...
% 7.77/1.81 Prover 6: Proving ...
% 7.77/1.81 Prover 1: Warning: ignoring some quantifiers
% 7.77/1.82 Prover 3: Warning: ignoring some quantifiers
% 8.60/1.88 Prover 3: Constructing countermodel ...
% 8.60/1.89 Prover 1: Constructing countermodel ...
% 9.88/2.08 Prover 2: proved (1447ms)
% 9.88/2.08
% 9.88/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.88/2.08
% 9.88/2.08 Prover 6: stopped
% 9.88/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.88/2.09 Prover 3: stopped
% 9.88/2.10 Prover 5: stopped
% 9.88/2.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.88/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.88/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.35/2.14 Prover 8: Preprocessing ...
% 10.70/2.16 Prover 11: Preprocessing ...
% 10.70/2.17 Prover 7: Preprocessing ...
% 10.70/2.18 Prover 10: Preprocessing ...
% 10.70/2.19 Prover 4: Warning: ignoring some quantifiers
% 10.70/2.24 Prover 7: Warning: ignoring some quantifiers
% 11.38/2.26 Prover 10: Warning: ignoring some quantifiers
% 11.38/2.26 Prover 7: Constructing countermodel ...
% 11.38/2.27 Prover 0: Proving ...
% 11.38/2.27 Prover 4: Constructing countermodel ...
% 11.38/2.28 Prover 0: stopped
% 11.38/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.68/2.29 Prover 10: Constructing countermodel ...
% 11.68/2.31 Prover 8: Warning: ignoring some quantifiers
% 11.68/2.33 Prover 8: Constructing countermodel ...
% 12.11/2.34 Prover 13: Preprocessing ...
% 12.66/2.43 Prover 10: Found proof (size 11)
% 12.66/2.43 Prover 10: proved (325ms)
% 12.66/2.43 Prover 4: stopped
% 12.66/2.43 Prover 1: stopped
% 12.66/2.43 Prover 7: Found proof (size 11)
% 12.66/2.43 Prover 7: proved (348ms)
% 12.66/2.43 Prover 8: stopped
% 12.66/2.45 Prover 13: Warning: ignoring some quantifiers
% 12.96/2.46 Prover 13: Constructing countermodel ...
% 12.96/2.47 Prover 13: stopped
% 13.38/2.61 Prover 11: Warning: ignoring some quantifiers
% 13.38/2.65 Prover 11: Constructing countermodel ...
% 13.74/2.66 Prover 11: stopped
% 13.74/2.66
% 13.74/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.74/2.66
% 13.74/2.66 % SZS output start Proof for theBenchmark
% 13.74/2.66 Assumptions after simplification:
% 13.74/2.66 ---------------------------------
% 13.74/2.66
% 13.74/2.67 (between_c_defn)
% 13.74/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1
% 13.74/2.68 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 13.74/2.68 inner_point(v2, v4) | ~ end_point(v3, v4) | ~ end_point(v1, v4) | ~
% 13.74/2.68 part_of(v4, v0) | between_c(v0, v1, v2, v3)) & ! [v0: $i] : ! [v1: $i] :
% 13.74/2.68 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 13.74/2.68 between_c(v0, v1, v2, v3) | ? [v4: $i] : ($i(v4) & inner_point(v2, v4) &
% 13.74/2.68 end_point(v3, v4) & end_point(v1, v4) & part_of(v4, v0))) & ! [v0: $i] :
% 13.74/2.68 ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 13.74/2.68 between_c(v0, v1, v2, v1))
% 13.74/2.68
% 13.74/2.68 (between_o_defn)
% 13.74/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 13.74/2.69 | ~ $i(v1) | ~ $i(v0) | ~ ordered_by(v0, v3, v2) | ~ ordered_by(v0, v2,
% 13.74/2.69 v1) | between_o(v0, v1, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.74/2.69 : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 13.74/2.69 ordered_by(v0, v2, v3) | ~ ordered_by(v0, v1, v2) | between_o(v0, v1, v2,
% 13.74/2.69 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 13.74/2.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v0, v1, v2, v3) |
% 13.74/2.69 ordered_by(v0, v3, v2) | ordered_by(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i]
% 13.74/2.69 : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.74/2.69 ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v3, v2) | ordered_by(v0, v1,
% 13.74/2.69 v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3)
% 13.74/2.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v0, v1, v2, v3) |
% 13.74/2.69 ordered_by(v0, v2, v3) | ordered_by(v0, v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 13.74/2.69 : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.74/2.69 ~ between_o(v0, v1, v2, v3) | ordered_by(v0, v2, v1) | ordered_by(v0, v1,
% 13.74/2.69 v2))
% 13.74/2.69
% 13.74/2.69 (o3)
% 13.74/2.69 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 13.74/2.69 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_c(v4,
% 13.74/2.69 v1, v2, v3) | between_o(v0, v1, v2, v3) | ? [v5: $i] : ($i(v5) & ( ~
% 13.74/2.69 incident_o(v5, v0) | ~ incident_c(v5, v4)) & (incident_o(v5, v0) |
% 13.74/2.69 incident_c(v5, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.74/2.69 [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v3,
% 13.74/2.69 v0, v1, v2) | ? [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) & ! [v5:
% 13.74/2.69 $i] : ( ~ $i(v5) | ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5:
% 13.74/2.69 $i] : ( ~ $i(v5) | ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 13.74/2.69
% 13.74/2.69 (theorem_4_5)
% 13.74/2.69 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 13.74/2.69 ordered_by(v0, v2, v1) & ordered_by(v0, v1, v2))
% 13.74/2.70
% 13.74/2.70 Further assumptions not needed in the proof:
% 13.74/2.70 --------------------------------------------
% 13.74/2.70 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 13.74/2.70 finish_point_defn, inner_point_defn, meet_defn, o1, o2, o4, o5, o6, open_defn,
% 13.74/2.70 part_of_defn, start_point_defn, sum_defn, underlying_curve_defn
% 13.74/2.70
% 13.74/2.70 Those formulas are unsatisfiable:
% 13.74/2.70 ---------------------------------
% 13.74/2.70
% 13.74/2.70 Begin of proof
% 13.74/2.70 |
% 13.74/2.70 | ALPHA: (between_c_defn) implies:
% 13.74/2.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 13.74/2.70 | $i(v0) | ~ between_c(v0, v1, v2, v1))
% 13.74/2.70 |
% 13.74/2.70 | ALPHA: (between_o_defn) implies:
% 13.74/2.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 13.74/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ ordered_by(v0, v3, v2) | ~
% 13.74/2.70 | ordered_by(v0, v2, v1) | between_o(v0, v1, v2, v3))
% 13.74/2.70 |
% 13.74/2.70 | ALPHA: (o3) implies:
% 13.74/2.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 13.74/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ between_o(v3, v0, v1, v2) | ?
% 13.74/2.70 | [v4: $i] : ($i(v4) & between_c(v4, v0, v1, v2) & ! [v5: $i] : ( ~
% 13.74/2.70 | $i(v5) | ~ incident_o(v5, v3) | incident_c(v5, v4)) & ! [v5:
% 13.74/2.70 | $i] : ( ~ $i(v5) | ~ incident_c(v5, v4) | incident_o(v5, v3))))
% 13.74/2.70 |
% 13.74/2.70 | DELTA: instantiating (theorem_4_5) with fresh symbols all_28_0, all_28_1,
% 13.74/2.70 | all_28_2 gives:
% 13.74/2.70 | (4) $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & ordered_by(all_28_2,
% 13.74/2.70 | all_28_0, all_28_1) & ordered_by(all_28_2, all_28_1, all_28_0)
% 13.74/2.70 |
% 13.74/2.70 | ALPHA: (4) implies:
% 13.74/2.70 | (5) ordered_by(all_28_2, all_28_1, all_28_0)
% 13.74/2.70 | (6) ordered_by(all_28_2, all_28_0, all_28_1)
% 14.13/2.70 | (7) $i(all_28_2)
% 14.13/2.70 | (8) $i(all_28_1)
% 14.13/2.70 | (9) $i(all_28_0)
% 14.13/2.70 |
% 14.13/2.71 | GROUND_INST: instantiating (2) with all_28_2, all_28_1, all_28_0, all_28_1,
% 14.13/2.71 | simplifying with (5), (6), (7), (8), (9) gives:
% 14.13/2.71 | (10) between_o(all_28_2, all_28_1, all_28_0, all_28_1)
% 14.13/2.71 |
% 14.13/2.71 | GROUND_INST: instantiating (3) with all_28_1, all_28_0, all_28_1, all_28_2,
% 14.13/2.71 | simplifying with (7), (8), (9), (10) gives:
% 14.13/2.71 | (11) ? [v0: $i] : ($i(v0) & between_c(v0, all_28_1, all_28_0, all_28_1) &
% 14.13/2.71 | ! [v1: $i] : ( ~ $i(v1) | ~ incident_o(v1, all_28_2) |
% 14.13/2.71 | incident_c(v1, v0)) & ! [v1: $i] : ( ~ $i(v1) | ~ incident_c(v1,
% 14.13/2.71 | v0) | incident_o(v1, all_28_2)))
% 14.13/2.71 |
% 14.13/2.71 | DELTA: instantiating (11) with fresh symbol all_55_0 gives:
% 14.13/2.71 | (12) $i(all_55_0) & between_c(all_55_0, all_28_1, all_28_0, all_28_1) & !
% 14.13/2.71 | [v0: $i] : ( ~ $i(v0) | ~ incident_o(v0, all_28_2) | incident_c(v0,
% 14.13/2.71 | all_55_0)) & ! [v0: $i] : ( ~ $i(v0) | ~ incident_c(v0,
% 14.13/2.71 | all_55_0) | incident_o(v0, all_28_2))
% 14.13/2.71 |
% 14.13/2.71 | ALPHA: (12) implies:
% 14.13/2.71 | (13) between_c(all_55_0, all_28_1, all_28_0, all_28_1)
% 14.13/2.71 | (14) $i(all_55_0)
% 14.13/2.71 |
% 14.13/2.71 | GROUND_INST: instantiating (1) with all_55_0, all_28_1, all_28_0, simplifying
% 14.13/2.71 | with (8), (9), (13), (14) gives:
% 14.13/2.71 | (15) $false
% 14.13/2.71 |
% 14.13/2.71 | CLOSE: (15) is inconsistent.
% 14.13/2.71 |
% 14.13/2.71 End of proof
% 14.13/2.71 % SZS output end Proof for theBenchmark
% 14.13/2.71
% 14.13/2.71 2101ms
%------------------------------------------------------------------------------