TSTP Solution File: GEO203+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO203+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 23:22:16 EDT 2023
% Result : Theorem 9.37s 2.33s
% Output : Proof 12.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 19:07:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/1.06 Prover 4: Preprocessing ...
% 2.16/1.07 Prover 1: Preprocessing ...
% 2.87/1.10 Prover 5: Preprocessing ...
% 2.87/1.10 Prover 2: Preprocessing ...
% 2.87/1.10 Prover 6: Preprocessing ...
% 2.87/1.10 Prover 3: Preprocessing ...
% 2.87/1.10 Prover 0: Preprocessing ...
% 4.36/1.32 Prover 5: Proving ...
% 4.36/1.33 Prover 2: Proving ...
% 4.36/1.34 Prover 6: Constructing countermodel ...
% 4.36/1.37 Prover 1: Constructing countermodel ...
% 4.36/1.37 Prover 3: Constructing countermodel ...
% 5.03/1.50 Prover 4: Constructing countermodel ...
% 5.61/1.58 Prover 0: Proving ...
% 6.52/1.63 Prover 6: gave up
% 6.52/1.65 Prover 3: gave up
% 6.52/1.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.52/1.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.24/1.74 Prover 7: Preprocessing ...
% 7.24/1.74 Prover 8: Preprocessing ...
% 7.89/1.80 Prover 7: Warning: ignoring some quantifiers
% 7.89/1.80 Prover 7: Constructing countermodel ...
% 7.89/1.87 Prover 1: gave up
% 7.89/1.88 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.57/1.89 Prover 8: Warning: ignoring some quantifiers
% 8.59/1.90 Prover 8: Constructing countermodel ...
% 8.69/1.92 Prover 9: Preprocessing ...
% 9.37/2.02 Prover 8: gave up
% 9.37/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.37/2.08 Prover 10: Preprocessing ...
% 9.37/2.14 Prover 10: Warning: ignoring some quantifiers
% 9.37/2.15 Prover 10: Constructing countermodel ...
% 9.37/2.21 Prover 9: Constructing countermodel ...
% 9.37/2.33 Prover 2: proved (1705ms)
% 9.37/2.33
% 9.37/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.37/2.33
% 9.37/2.34 Prover 0: stopped
% 10.58/2.34 Prover 9: stopped
% 10.58/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.58/2.36 Prover 5: stopped
% 10.58/2.36 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.58/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.58/2.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.58/2.39 Prover 13: Preprocessing ...
% 10.58/2.40 Prover 7: Found proof (size 22)
% 10.58/2.40 Prover 7: proved (747ms)
% 10.58/2.40 Prover 4: stopped
% 10.58/2.40 Prover 10: stopped
% 10.58/2.40 Prover 19: Preprocessing ...
% 10.58/2.41 Prover 16: Preprocessing ...
% 10.58/2.41 Prover 13: stopped
% 10.58/2.42 Prover 11: Preprocessing ...
% 10.58/2.43 Prover 16: stopped
% 12.34/2.45 Prover 11: stopped
% 12.34/2.49 Prover 19: Warning: ignoring some quantifiers
% 12.34/2.49 Prover 19: Constructing countermodel ...
% 12.34/2.50 Prover 19: stopped
% 12.34/2.50
% 12.34/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.34/2.50
% 12.65/2.51 % SZS output start Proof for theBenchmark
% 12.65/2.51 Assumptions after simplification:
% 12.65/2.51 ---------------------------------
% 12.65/2.51
% 12.65/2.51 (apart1)
% 12.65/2.52 ! [v0: $i] : ( ~ $i(v0) | ~ distinct_points(v0, v0))
% 12.65/2.52
% 12.65/2.52 (con)
% 12.65/2.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 12.65/2.56 $i] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 &
% 12.91/2.56 line_connecting(v3, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 12.91/2.56 $i(v0) & convergent_lines(v0, v2) & convergent_lines(v0, v1) &
% 12.91/2.56 distinct_lines(v5, v0) & distinct_points(v3, v4))
% 12.91/2.56
% 12.91/2.56 (con1)
% 12.91/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.91/2.57 (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.91/2.57 apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 12.91/2.57 distinct_points(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.91/2.57 $i] : ( ~ (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 12.91/2.57 | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 12.91/2.57 distinct_points(v2, v0))
% 12.91/2.57
% 12.91/2.57 (con2)
% 12.91/2.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.91/2.57 (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 12.91/2.57 apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) |
% 12.91/2.57 distinct_points(v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.91/2.57 $i] : ( ~ (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.91/2.57 $i(v0) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 12.91/2.57 distinct_points(v2, v3))
% 12.91/2.57
% 12.91/2.58 (cu1)
% 12.91/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 12.91/2.58 | ~ $i(v1) | ~ $i(v0) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0,
% 12.91/2.58 v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) |
% 12.91/2.58 apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 12.91/2.58
% 12.91/2.58 Further assumptions not needed in the proof:
% 12.91/2.58 --------------------------------------------
% 12.91/2.58 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3
% 12.91/2.58
% 12.91/2.58 Those formulas are unsatisfiable:
% 12.91/2.58 ---------------------------------
% 12.91/2.58
% 12.91/2.58 Begin of proof
% 12.91/2.58 |
% 12.91/2.58 | ALPHA: (con1) implies:
% 12.91/2.59 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.91/2.59 | (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.91/2.59 | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 12.91/2.59 | distinct_points(v2, v0))
% 12.91/2.59 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.91/2.59 | (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.91/2.59 | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 12.91/2.59 | distinct_points(v2, v1))
% 12.91/2.59 |
% 12.91/2.59 | ALPHA: (con2) implies:
% 12.91/2.59 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.91/2.59 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 12.91/2.59 | | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 12.91/2.59 | distinct_points(v2, v3))
% 12.91/2.59 |
% 12.91/2.59 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 12.91/2.59 | all_20_3, all_20_4, all_20_5 gives:
% 12.91/2.59 | (4) intersection_point(all_20_5, all_20_3) = all_20_1 &
% 12.91/2.59 | intersection_point(all_20_5, all_20_4) = all_20_2 &
% 12.91/2.59 | line_connecting(all_20_2, all_20_1) = all_20_0 & $i(all_20_0) &
% 12.91/2.59 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 12.91/2.59 | $i(all_20_5) & convergent_lines(all_20_5, all_20_3) &
% 12.91/2.60 | convergent_lines(all_20_5, all_20_4) & distinct_lines(all_20_0,
% 12.91/2.60 | all_20_5) & distinct_points(all_20_2, all_20_1)
% 12.91/2.60 |
% 12.91/2.60 | ALPHA: (4) implies:
% 12.91/2.60 | (5) distinct_points(all_20_2, all_20_1)
% 12.91/2.60 | (6) distinct_lines(all_20_0, all_20_5)
% 12.91/2.60 | (7) convergent_lines(all_20_5, all_20_4)
% 12.91/2.60 | (8) convergent_lines(all_20_5, all_20_3)
% 12.91/2.60 | (9) $i(all_20_5)
% 12.91/2.60 | (10) $i(all_20_4)
% 12.91/2.60 | (11) $i(all_20_3)
% 12.91/2.60 | (12) $i(all_20_2)
% 12.91/2.60 | (13) $i(all_20_1)
% 12.91/2.60 | (14) $i(all_20_0)
% 12.91/2.60 | (15) line_connecting(all_20_2, all_20_1) = all_20_0
% 12.91/2.60 | (16) intersection_point(all_20_5, all_20_4) = all_20_2
% 12.91/2.60 | (17) intersection_point(all_20_5, all_20_3) = all_20_1
% 12.91/2.60 |
% 12.91/2.60 | GROUND_INST: instantiating (apart1) with all_20_2, simplifying with (12)
% 12.91/2.60 | gives:
% 12.91/2.60 | (18) ~ distinct_points(all_20_2, all_20_2)
% 12.91/2.60 |
% 12.91/2.60 | GROUND_INST: instantiating (cu1) with all_20_2, all_20_1, all_20_0, all_20_5,
% 12.91/2.60 | simplifying with (5), (6), (9), (12), (13), (14) gives:
% 12.91/2.60 | (19) apart_point_and_line(all_20_1, all_20_0) |
% 12.91/2.60 | apart_point_and_line(all_20_1, all_20_5) |
% 12.91/2.60 | apart_point_and_line(all_20_2, all_20_0) |
% 12.91/2.60 | apart_point_and_line(all_20_2, all_20_5)
% 12.91/2.60 |
% 12.91/2.60 | BETA: splitting (19) gives:
% 12.91/2.60 |
% 12.91/2.60 | Case 1:
% 12.91/2.60 | |
% 12.91/2.60 | | (20) apart_point_and_line(all_20_1, all_20_0)
% 12.91/2.61 | |
% 12.91/2.61 | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_20_1, all_20_0,
% 12.91/2.61 | | simplifying with (5), (12), (13), (15), (20) gives:
% 12.91/2.61 | | (21) distinct_points(all_20_1, all_20_1)
% 12.91/2.61 | |
% 12.91/2.61 | | GROUND_INST: instantiating (apart1) with all_20_1, simplifying with (13),
% 12.91/2.61 | | (21) gives:
% 12.91/2.61 | | (22) $false
% 12.91/2.61 | |
% 12.91/2.61 | | CLOSE: (22) is inconsistent.
% 12.91/2.61 | |
% 12.91/2.61 | Case 2:
% 12.91/2.61 | |
% 12.91/2.61 | | (23) apart_point_and_line(all_20_1, all_20_5) |
% 12.91/2.61 | | apart_point_and_line(all_20_2, all_20_0) |
% 12.91/2.61 | | apart_point_and_line(all_20_2, all_20_5)
% 12.91/2.61 | |
% 12.91/2.61 | | BETA: splitting (23) gives:
% 12.91/2.61 | |
% 12.91/2.61 | | Case 1:
% 12.91/2.61 | | |
% 12.91/2.61 | | | (24) apart_point_and_line(all_20_1, all_20_5)
% 12.91/2.61 | | |
% 12.91/2.61 | | | GROUND_INST: instantiating (3) with all_20_5, all_20_3, all_20_1,
% 12.91/2.61 | | | all_20_1, simplifying with (8), (9), (11), (13), (17), (24)
% 12.91/2.61 | | | gives:
% 12.91/2.61 | | | (25) distinct_points(all_20_1, all_20_1)
% 12.91/2.61 | | |
% 12.91/2.61 | | | GROUND_INST: instantiating (apart1) with all_20_1, simplifying with (13),
% 12.91/2.61 | | | (25) gives:
% 12.91/2.61 | | | (26) $false
% 12.91/2.61 | | |
% 12.91/2.61 | | | CLOSE: (26) is inconsistent.
% 12.91/2.61 | | |
% 12.91/2.62 | | Case 2:
% 12.91/2.62 | | |
% 12.91/2.62 | | | (27) apart_point_and_line(all_20_2, all_20_0) |
% 12.91/2.62 | | | apart_point_and_line(all_20_2, all_20_5)
% 12.91/2.62 | | |
% 12.91/2.62 | | | BETA: splitting (27) gives:
% 12.91/2.62 | | |
% 12.91/2.62 | | | Case 1:
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | (28) apart_point_and_line(all_20_2, all_20_0)
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | GROUND_INST: instantiating (1) with all_20_2, all_20_1, all_20_2,
% 12.91/2.62 | | | | all_20_0, simplifying with (5), (12), (13), (15), (18),
% 12.91/2.62 | | | | (28) gives:
% 12.91/2.62 | | | | (29) $false
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | CLOSE: (29) is inconsistent.
% 12.91/2.62 | | | |
% 12.91/2.62 | | | Case 2:
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | (30) apart_point_and_line(all_20_2, all_20_5)
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | GROUND_INST: instantiating (3) with all_20_5, all_20_4, all_20_2,
% 12.91/2.62 | | | | all_20_2, simplifying with (7), (9), (10), (12), (16),
% 12.91/2.62 | | | | (18), (30) gives:
% 12.91/2.62 | | | | (31) $false
% 12.91/2.62 | | | |
% 12.91/2.62 | | | | CLOSE: (31) is inconsistent.
% 12.91/2.62 | | | |
% 12.91/2.62 | | | End of split
% 12.91/2.62 | | |
% 12.91/2.62 | | End of split
% 12.91/2.62 | |
% 12.91/2.62 | End of split
% 12.91/2.62 |
% 12.91/2.62 End of proof
% 12.91/2.62 % SZS output end Proof for theBenchmark
% 12.91/2.62
% 12.91/2.62 2014ms
%------------------------------------------------------------------------------