TSTP Solution File: GEO202+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO202+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 : n007.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 23:22:15 EDT 2023
% Result : Theorem 9.21s 2.04s
% Output : Proof 9.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO202+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 20:30:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.56/0.62 ________ _____
% 0.56/0.62 ___ __ \_________(_)________________________________
% 0.56/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.56/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.56/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.56/0.62
% 0.56/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.56/0.62 (2023-06-19)
% 0.56/0.62
% 0.56/0.62 (c) Philipp Rümmer, 2009-2023
% 0.56/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.56/0.62 Amanda Stjerna.
% 0.56/0.62 Free software under BSD-3-Clause.
% 0.56/0.62
% 0.56/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.56/0.62
% 0.56/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.63 Running up to 7 provers in parallel.
% 0.70/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.67/1.09 Prover 4: Preprocessing ...
% 2.67/1.09 Prover 1: Preprocessing ...
% 2.67/1.12 Prover 5: Preprocessing ...
% 2.67/1.12 Prover 2: Preprocessing ...
% 2.67/1.12 Prover 6: Preprocessing ...
% 2.67/1.12 Prover 0: Preprocessing ...
% 2.67/1.13 Prover 3: Preprocessing ...
% 4.75/1.37 Prover 5: Proving ...
% 4.75/1.37 Prover 1: Constructing countermodel ...
% 4.75/1.38 Prover 2: Proving ...
% 4.75/1.38 Prover 6: Constructing countermodel ...
% 4.75/1.38 Prover 3: Constructing countermodel ...
% 5.41/1.46 Prover 4: Constructing countermodel ...
% 5.68/1.50 Prover 1: gave up
% 5.68/1.50 Prover 3: gave up
% 5.68/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.68/1.50 Prover 0: Proving ...
% 5.68/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.95/1.54 Prover 8: Preprocessing ...
% 5.97/1.54 Prover 6: gave up
% 5.97/1.54 Prover 7: Preprocessing ...
% 5.97/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.97/1.56 Prover 9: Preprocessing ...
% 5.97/1.59 Prover 7: Warning: ignoring some quantifiers
% 6.51/1.61 Prover 7: Constructing countermodel ...
% 6.93/1.67 Prover 8: Warning: ignoring some quantifiers
% 6.93/1.70 Prover 8: Constructing countermodel ...
% 6.93/1.76 Prover 9: Constructing countermodel ...
% 7.66/1.77 Prover 8: gave up
% 7.66/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.87/1.79 Prover 10: Preprocessing ...
% 8.12/1.84 Prover 10: Warning: ignoring some quantifiers
% 8.12/1.85 Prover 10: Constructing countermodel ...
% 9.21/2.03 Prover 7: Found proof (size 24)
% 9.21/2.03 Prover 7: proved (535ms)
% 9.21/2.03 Prover 9: stopped
% 9.21/2.03 Prover 10: stopped
% 9.21/2.03 Prover 4: stopped
% 9.21/2.04 Prover 5: stopped
% 9.21/2.04 Prover 2: stopped
% 9.21/2.04 Prover 0: stopped
% 9.21/2.04
% 9.21/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.21/2.04
% 9.21/2.04 % SZS output start Proof for theBenchmark
% 9.21/2.04 Assumptions after simplification:
% 9.21/2.04 ---------------------------------
% 9.21/2.04
% 9.21/2.04 (apart1)
% 9.21/2.05 ! [v0: $i] : ( ~ $i(v0) | ~ distinct_points(v0, v0))
% 9.21/2.05
% 9.21/2.05 (ceq3)
% 9.21/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ convergent_lines(v0,
% 9.21/2.05 v1) | distinct_lines(v0, v1))
% 9.21/2.05
% 9.21/2.05 (con)
% 9.83/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 9.83/2.07 $i] : (intersection_point(v3, v4) = v5 & line_connecting(v0, v2) = v4 &
% 9.83/2.07 line_connecting(v0, v1) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 9.83/2.07 $i(v0) & convergent_lines(v3, v4) & distinct_points(v5, v0) &
% 9.83/2.07 distinct_points(v0, v2) & distinct_points(v0, v1))
% 9.83/2.07
% 9.83/2.07 (con1)
% 9.83/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.83/2.08 (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.83/2.08 apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 9.83/2.08 distinct_points(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 9.83/2.08 $i] : ( ~ (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 9.83/2.08 | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 9.83/2.08 distinct_points(v2, v0))
% 9.83/2.08
% 9.83/2.08 (con2)
% 9.83/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.83/2.08 (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 9.83/2.08 apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) |
% 9.83/2.08 distinct_points(v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 9.83/2.08 $i] : ( ~ (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 9.83/2.08 $i(v0) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 9.83/2.08 distinct_points(v2, v3))
% 9.83/2.08
% 9.83/2.08 (cu1)
% 9.83/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 9.83/2.08 | ~ $i(v1) | ~ $i(v0) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0,
% 9.83/2.08 v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) |
% 9.83/2.08 apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 9.83/2.08
% 9.83/2.08 Further assumptions not needed in the proof:
% 9.83/2.08 --------------------------------------------
% 9.83/2.08 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2
% 9.83/2.08
% 9.83/2.08 Those formulas are unsatisfiable:
% 9.83/2.08 ---------------------------------
% 9.83/2.08
% 9.83/2.08 Begin of proof
% 9.83/2.08 |
% 9.83/2.08 | ALPHA: (con1) implies:
% 9.83/2.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.83/2.09 | (line_connecting(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 9.83/2.09 | ~ apart_point_and_line(v2, v3) | ~ distinct_points(v0, v1) |
% 9.83/2.09 | distinct_points(v2, v0))
% 9.83/2.09 |
% 9.83/2.09 | ALPHA: (con2) implies:
% 9.83/2.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.83/2.09 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 9.83/2.09 | | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) |
% 9.83/2.09 | distinct_points(v2, v3))
% 9.83/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.83/2.09 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 9.83/2.09 | | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) |
% 9.83/2.09 | distinct_points(v2, v3))
% 9.83/2.09 |
% 9.83/2.09 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 9.83/2.09 | all_20_3, all_20_4, all_20_5 gives:
% 9.83/2.09 | (4) intersection_point(all_20_2, all_20_1) = all_20_0 &
% 9.83/2.09 | line_connecting(all_20_5, all_20_3) = all_20_1 &
% 9.83/2.09 | line_connecting(all_20_5, all_20_4) = all_20_2 & $i(all_20_0) &
% 9.83/2.09 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 9.83/2.09 | $i(all_20_5) & convergent_lines(all_20_2, all_20_1) &
% 9.83/2.09 | distinct_points(all_20_0, all_20_5) & distinct_points(all_20_5,
% 9.83/2.09 | all_20_3) & distinct_points(all_20_5, all_20_4)
% 9.83/2.09 |
% 9.83/2.09 | ALPHA: (4) implies:
% 9.83/2.09 | (5) distinct_points(all_20_5, all_20_4)
% 9.83/2.09 | (6) distinct_points(all_20_5, all_20_3)
% 9.97/2.09 | (7) distinct_points(all_20_0, all_20_5)
% 9.97/2.09 | (8) convergent_lines(all_20_2, all_20_1)
% 9.97/2.09 | (9) $i(all_20_5)
% 9.97/2.09 | (10) $i(all_20_4)
% 9.97/2.09 | (11) $i(all_20_3)
% 9.97/2.09 | (12) $i(all_20_2)
% 9.97/2.09 | (13) $i(all_20_1)
% 9.97/2.09 | (14) $i(all_20_0)
% 9.97/2.09 | (15) line_connecting(all_20_5, all_20_4) = all_20_2
% 9.97/2.09 | (16) line_connecting(all_20_5, all_20_3) = all_20_1
% 9.97/2.10 | (17) intersection_point(all_20_2, all_20_1) = all_20_0
% 9.97/2.10 |
% 9.97/2.10 | GROUND_INST: instantiating (apart1) with all_20_5, simplifying with (9) gives:
% 9.97/2.10 | (18) ~ distinct_points(all_20_5, all_20_5)
% 9.97/2.10 |
% 9.97/2.10 | GROUND_INST: instantiating (ceq3) with all_20_2, all_20_1, simplifying with
% 9.97/2.10 | (8), (12), (13) gives:
% 9.97/2.10 | (19) distinct_lines(all_20_2, all_20_1)
% 9.97/2.10 |
% 9.97/2.10 | GROUND_INST: instantiating (cu1) with all_20_0, all_20_5, all_20_2, all_20_1,
% 9.97/2.10 | simplifying with (7), (9), (12), (13), (14), (19) gives:
% 9.97/2.10 | (20) apart_point_and_line(all_20_0, all_20_1) |
% 9.97/2.10 | apart_point_and_line(all_20_0, all_20_2) |
% 9.97/2.10 | apart_point_and_line(all_20_5, all_20_1) |
% 9.97/2.10 | apart_point_and_line(all_20_5, all_20_2)
% 9.97/2.10 |
% 9.97/2.10 | BETA: splitting (20) gives:
% 9.97/2.10 |
% 9.97/2.10 | Case 1:
% 9.97/2.10 | |
% 9.97/2.10 | | (21) apart_point_and_line(all_20_0, all_20_1)
% 9.97/2.10 | |
% 9.97/2.10 | | GROUND_INST: instantiating (3) with all_20_2, all_20_1, all_20_0, all_20_0,
% 9.97/2.10 | | simplifying with (8), (12), (13), (14), (17), (21) gives:
% 9.97/2.10 | | (22) distinct_points(all_20_0, all_20_0)
% 9.97/2.10 | |
% 9.97/2.10 | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (14),
% 9.97/2.10 | | (22) gives:
% 9.97/2.10 | | (23) $false
% 9.97/2.10 | |
% 9.97/2.10 | | CLOSE: (23) is inconsistent.
% 9.97/2.10 | |
% 9.97/2.10 | Case 2:
% 9.97/2.10 | |
% 9.97/2.10 | | (24) apart_point_and_line(all_20_0, all_20_2) |
% 9.97/2.10 | | apart_point_and_line(all_20_5, all_20_1) |
% 9.97/2.10 | | apart_point_and_line(all_20_5, all_20_2)
% 9.97/2.10 | |
% 9.97/2.10 | | BETA: splitting (24) gives:
% 9.97/2.10 | |
% 9.97/2.10 | | Case 1:
% 9.97/2.10 | | |
% 9.97/2.10 | | | (25) apart_point_and_line(all_20_0, all_20_2)
% 9.97/2.10 | | |
% 9.97/2.10 | | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_20_0,
% 9.97/2.10 | | | all_20_0, simplifying with (8), (12), (13), (14), (17), (25)
% 9.97/2.10 | | | gives:
% 9.97/2.10 | | | (26) distinct_points(all_20_0, all_20_0)
% 9.97/2.10 | | |
% 9.97/2.10 | | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (14),
% 9.97/2.10 | | | (26) gives:
% 9.97/2.10 | | | (27) $false
% 9.97/2.10 | | |
% 9.97/2.10 | | | CLOSE: (27) is inconsistent.
% 9.97/2.10 | | |
% 9.97/2.10 | | Case 2:
% 9.97/2.10 | | |
% 9.97/2.10 | | | (28) apart_point_and_line(all_20_5, all_20_1) |
% 9.97/2.10 | | | apart_point_and_line(all_20_5, all_20_2)
% 9.97/2.10 | | |
% 9.97/2.10 | | | BETA: splitting (28) gives:
% 9.97/2.10 | | |
% 9.97/2.10 | | | Case 1:
% 9.97/2.10 | | | |
% 9.97/2.10 | | | | (29) apart_point_and_line(all_20_5, all_20_1)
% 9.97/2.10 | | | |
% 9.97/2.10 | | | | GROUND_INST: instantiating (1) with all_20_5, all_20_3, all_20_5,
% 9.97/2.10 | | | | all_20_1, simplifying with (6), (9), (11), (16), (18), (29)
% 9.97/2.10 | | | | gives:
% 9.97/2.11 | | | | (30) $false
% 9.97/2.11 | | | |
% 9.97/2.11 | | | | CLOSE: (30) is inconsistent.
% 9.97/2.11 | | | |
% 9.97/2.11 | | | Case 2:
% 9.97/2.11 | | | |
% 9.97/2.11 | | | | (31) apart_point_and_line(all_20_5, all_20_2)
% 9.97/2.11 | | | |
% 9.97/2.11 | | | | GROUND_INST: instantiating (1) with all_20_5, all_20_4, all_20_5,
% 9.97/2.11 | | | | all_20_2, simplifying with (5), (9), (10), (15), (18), (31)
% 9.97/2.11 | | | | gives:
% 9.97/2.11 | | | | (32) $false
% 9.97/2.11 | | | |
% 9.97/2.11 | | | | CLOSE: (32) is inconsistent.
% 9.97/2.11 | | | |
% 9.97/2.11 | | | End of split
% 9.97/2.11 | | |
% 9.97/2.11 | | End of split
% 9.97/2.11 | |
% 9.97/2.11 | End of split
% 9.97/2.11 |
% 9.97/2.11 End of proof
% 9.97/2.11 % SZS output end Proof for theBenchmark
% 9.97/2.11
% 9.97/2.11 1488ms
%------------------------------------------------------------------------------