TSTP Solution File: GEO186+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO186+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 : n031.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 23:22:00 EDT 2023
% Result : Theorem 7.22s 1.75s
% Output : Proof 8.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO186+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 23:27:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.63/0.63 ________ _____
% 0.63/0.63 ___ __ \_________(_)________________________________
% 0.63/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.63/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.63/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.63/0.63
% 0.63/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.63/0.63 (2023-06-19)
% 0.63/0.63
% 0.63/0.63 (c) Philipp Rümmer, 2009-2023
% 0.63/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.63/0.63 Amanda Stjerna.
% 0.63/0.63 Free software under BSD-3-Clause.
% 0.63/0.63
% 0.63/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.63/0.63
% 0.63/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.65 Running up to 7 provers in parallel.
% 0.77/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.77/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.77/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.77/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.77/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.77/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.77/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.07 Prover 4: Preprocessing ...
% 2.58/1.07 Prover 1: Preprocessing ...
% 2.80/1.12 Prover 2: Preprocessing ...
% 2.80/1.12 Prover 5: Preprocessing ...
% 2.80/1.12 Prover 0: Preprocessing ...
% 2.80/1.12 Prover 3: Preprocessing ...
% 2.80/1.12 Prover 6: Preprocessing ...
% 4.56/1.33 Prover 5: Proving ...
% 4.56/1.35 Prover 3: Constructing countermodel ...
% 4.56/1.35 Prover 2: Proving ...
% 4.79/1.36 Prover 1: Constructing countermodel ...
% 4.79/1.39 Prover 6: Constructing countermodel ...
% 5.37/1.46 Prover 3: gave up
% 5.37/1.46 Prover 6: gave up
% 5.37/1.47 Prover 1: gave up
% 5.70/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.70/1.47 Prover 4: Constructing countermodel ...
% 5.70/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.70/1.47 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.70/1.51 Prover 9: Preprocessing ...
% 5.70/1.52 Prover 7: Preprocessing ...
% 5.70/1.53 Prover 8: Preprocessing ...
% 5.70/1.53 Prover 0: Proving ...
% 6.23/1.56 Prover 7: Warning: ignoring some quantifiers
% 6.43/1.57 Prover 7: Constructing countermodel ...
% 6.82/1.62 Prover 8: Warning: ignoring some quantifiers
% 6.82/1.63 Prover 8: Constructing countermodel ...
% 7.22/1.70 Prover 8: gave up
% 7.22/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.22/1.71 Prover 9: Constructing countermodel ...
% 7.22/1.74 Prover 10: Preprocessing ...
% 7.22/1.75 Prover 2: proved (1082ms)
% 7.22/1.75
% 7.22/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/1.75
% 7.22/1.75 Prover 9: stopped
% 7.79/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.79/1.75 Prover 0: stopped
% 7.79/1.77 Prover 5: stopped
% 7.79/1.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.79/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.79/1.79 Prover 10: Warning: ignoring some quantifiers
% 7.79/1.79 Prover 13: Preprocessing ...
% 7.79/1.79 Prover 11: Preprocessing ...
% 7.79/1.79 Prover 10: Constructing countermodel ...
% 7.79/1.79 Prover 16: Preprocessing ...
% 8.12/1.80 Prover 7: Found proof (size 13)
% 8.12/1.80 Prover 7: proved (337ms)
% 8.12/1.80 Prover 4: stopped
% 8.12/1.80 Prover 10: stopped
% 8.12/1.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.12/1.81 Prover 13: Warning: ignoring some quantifiers
% 8.12/1.82 Prover 13: Constructing countermodel ...
% 8.12/1.82 Prover 19: Preprocessing ...
% 8.12/1.82 Prover 13: stopped
% 8.12/1.82 Prover 11: stopped
% 8.12/1.82 Prover 16: Warning: ignoring some quantifiers
% 8.12/1.82 Prover 16: Constructing countermodel ...
% 8.12/1.83 Prover 16: stopped
% 8.40/1.87 Prover 19: Warning: ignoring some quantifiers
% 8.40/1.88 Prover 19: Constructing countermodel ...
% 8.40/1.88 Prover 19: stopped
% 8.40/1.88
% 8.40/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.40/1.88
% 8.40/1.89 % SZS output start Proof for theBenchmark
% 8.40/1.89 Assumptions after simplification:
% 8.40/1.89 ---------------------------------
% 8.40/1.89
% 8.40/1.89 (apart1)
% 8.40/1.89 ! [v0: $i] : ( ~ $i(v0) | ~ distinct_points(v0, v0))
% 8.40/1.89
% 8.40/1.89 (ceq3)
% 8.40/1.89 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ convergent_lines(v0,
% 8.40/1.89 v1) | distinct_lines(v0, v1))
% 8.40/1.89
% 8.40/1.89 (con)
% 8.40/1.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 8.40/1.92 (intersection_point(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 8.40/1.92 & convergent_lines(v2, v3) & distinct_points(v0, v4) & distinct_points(v0,
% 8.40/1.92 v1) & ~ apart_point_and_line(v0, v3) & ~ apart_point_and_line(v0, v2))
% 8.40/1.92
% 8.40/1.92 (con2)
% 8.40/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.40/1.92 (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 8.40/1.92 apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) |
% 8.40/1.92 distinct_points(v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.40/1.92 $i] : ( ~ (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 8.40/1.92 $i(v0) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 8.40/1.92 distinct_points(v2, v3))
% 8.40/1.92
% 8.40/1.92 (cu1)
% 8.40/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 8.40/1.92 | ~ $i(v1) | ~ $i(v0) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0,
% 8.40/1.92 v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) |
% 8.40/1.92 apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 8.40/1.92
% 8.40/1.92 Further assumptions not needed in the proof:
% 8.40/1.92 --------------------------------------------
% 8.40/1.92 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, con1
% 8.40/1.92
% 8.40/1.92 Those formulas are unsatisfiable:
% 8.40/1.92 ---------------------------------
% 8.40/1.92
% 8.40/1.92 Begin of proof
% 8.40/1.92 |
% 8.40/1.92 | ALPHA: (con2) implies:
% 8.40/1.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.40/1.92 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.40/1.92 | | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 8.40/1.92 | distinct_points(v2, v3))
% 8.40/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.40/1.93 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.40/1.93 | | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) |
% 8.40/1.93 | distinct_points(v2, v3))
% 8.40/1.93 |
% 8.40/1.93 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 8.40/1.93 | all_20_3, all_20_4 gives:
% 8.40/1.93 | (3) intersection_point(all_20_2, all_20_1) = all_20_0 & $i(all_20_0) &
% 8.40/1.93 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 8.40/1.93 | convergent_lines(all_20_2, all_20_1) & distinct_points(all_20_4,
% 8.40/1.93 | all_20_0) & distinct_points(all_20_4, all_20_3) & ~
% 8.40/1.93 | apart_point_and_line(all_20_4, all_20_1) & ~
% 8.40/1.93 | apart_point_and_line(all_20_4, all_20_2)
% 8.40/1.93 |
% 8.40/1.93 | ALPHA: (3) implies:
% 8.40/1.93 | (4) ~ apart_point_and_line(all_20_4, all_20_2)
% 8.40/1.93 | (5) ~ apart_point_and_line(all_20_4, all_20_1)
% 8.40/1.93 | (6) distinct_points(all_20_4, all_20_0)
% 8.40/1.93 | (7) convergent_lines(all_20_2, all_20_1)
% 8.40/1.93 | (8) $i(all_20_4)
% 8.40/1.93 | (9) $i(all_20_2)
% 8.40/1.93 | (10) $i(all_20_1)
% 8.40/1.93 | (11) $i(all_20_0)
% 8.40/1.93 | (12) intersection_point(all_20_2, all_20_1) = all_20_0
% 8.40/1.93 |
% 8.40/1.93 | GROUND_INST: instantiating (ceq3) with all_20_2, all_20_1, simplifying with
% 8.40/1.93 | (7), (9), (10) gives:
% 8.40/1.93 | (13) distinct_lines(all_20_2, all_20_1)
% 8.40/1.93 |
% 8.40/1.93 | GROUND_INST: instantiating (cu1) with all_20_4, all_20_0, all_20_2, all_20_1,
% 8.40/1.93 | simplifying with (4), (5), (6), (8), (9), (10), (11), (13) gives:
% 8.40/1.93 | (14) apart_point_and_line(all_20_0, all_20_1) |
% 8.40/1.93 | apart_point_and_line(all_20_0, all_20_2)
% 8.40/1.93 |
% 8.40/1.93 | BETA: splitting (14) gives:
% 8.40/1.93 |
% 8.40/1.93 | Case 1:
% 8.40/1.93 | |
% 8.40/1.93 | | (15) apart_point_and_line(all_20_0, all_20_1)
% 8.40/1.93 | |
% 8.40/1.93 | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_20_0, all_20_0,
% 8.40/1.93 | | simplifying with (7), (9), (10), (11), (12), (15) gives:
% 8.40/1.93 | | (16) distinct_points(all_20_0, all_20_0)
% 8.40/1.93 | |
% 8.40/1.93 | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (11),
% 8.40/1.93 | | (16) gives:
% 8.40/1.93 | | (17) $false
% 8.40/1.94 | |
% 8.40/1.94 | | CLOSE: (17) is inconsistent.
% 8.40/1.94 | |
% 8.40/1.94 | Case 2:
% 8.40/1.94 | |
% 8.40/1.94 | | (18) apart_point_and_line(all_20_0, all_20_2)
% 8.40/1.94 | |
% 8.40/1.94 | | GROUND_INST: instantiating (1) with all_20_2, all_20_1, all_20_0, all_20_0,
% 8.40/1.94 | | simplifying with (7), (9), (10), (11), (12), (18) gives:
% 8.40/1.94 | | (19) distinct_points(all_20_0, all_20_0)
% 8.40/1.94 | |
% 8.40/1.94 | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (11),
% 8.40/1.94 | | (19) gives:
% 8.40/1.94 | | (20) $false
% 8.40/1.94 | |
% 8.40/1.94 | | CLOSE: (20) is inconsistent.
% 8.40/1.94 | |
% 8.40/1.94 | End of split
% 8.40/1.94 |
% 8.40/1.94 End of proof
% 8.40/1.94 % SZS output end Proof for theBenchmark
% 8.40/1.94
% 8.40/1.94 1301ms
%------------------------------------------------------------------------------