TSTP Solution File: GEO200+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO200+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 : n018.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 23:22:13 EDT 2023
% Result : Theorem 7.21s 1.71s
% Output : Proof 8.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO200+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n018.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 22:24:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.20/1.06 Prover 4: Preprocessing ...
% 2.20/1.06 Prover 1: Preprocessing ...
% 2.64/1.10 Prover 3: Preprocessing ...
% 2.64/1.10 Prover 0: Preprocessing ...
% 2.64/1.10 Prover 2: Preprocessing ...
% 2.64/1.10 Prover 6: Preprocessing ...
% 2.64/1.10 Prover 5: Preprocessing ...
% 4.29/1.32 Prover 5: Proving ...
% 4.29/1.32 Prover 2: Proving ...
% 4.29/1.33 Prover 3: Constructing countermodel ...
% 4.29/1.34 Prover 6: Constructing countermodel ...
% 4.29/1.36 Prover 1: Constructing countermodel ...
% 4.80/1.45 Prover 4: Constructing countermodel ...
% 4.80/1.46 Prover 0: Proving ...
% 5.49/1.57 Prover 6: gave up
% 5.73/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.47/1.62 Prover 7: Preprocessing ...
% 6.47/1.66 Prover 7: Warning: ignoring some quantifiers
% 6.47/1.67 Prover 7: Constructing countermodel ...
% 7.21/1.71 Prover 3: proved (1072ms)
% 7.21/1.71
% 7.21/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.21/1.71
% 7.21/1.71 Prover 5: stopped
% 7.21/1.71 Prover 2: stopped
% 7.21/1.72 Prover 0: stopped
% 7.21/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.21/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.21/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.21/1.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.21/1.73 Prover 1: Found proof (size 93)
% 7.21/1.73 Prover 1: proved (1099ms)
% 7.21/1.73 Prover 4: stopped
% 7.21/1.73 Prover 7: stopped
% 7.21/1.75 Prover 10: Preprocessing ...
% 7.21/1.75 Prover 8: Preprocessing ...
% 7.21/1.75 Prover 11: Preprocessing ...
% 7.21/1.75 Prover 13: Preprocessing ...
% 7.21/1.76 Prover 10: stopped
% 7.21/1.77 Prover 13: stopped
% 7.21/1.78 Prover 11: stopped
% 7.83/1.79 Prover 8: Warning: ignoring some quantifiers
% 7.83/1.80 Prover 8: Constructing countermodel ...
% 7.83/1.80 Prover 8: stopped
% 7.83/1.80
% 7.83/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.83/1.80
% 7.83/1.82 % SZS output start Proof for theBenchmark
% 7.83/1.82 Assumptions after simplification:
% 7.83/1.82 ---------------------------------
% 7.83/1.82
% 7.83/1.82 (apart1)
% 7.83/1.86 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 7.83/1.86
% 7.83/1.86 (apart4)
% 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.83/1.86 (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | ~
% 7.83/1.86 $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v1, v2) = 0)
% 7.83/1.86
% 7.83/1.86 (ceq1)
% 7.83/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.83/1.86 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~
% 7.83/1.86 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0)
% 7.83/1.86
% 7.83/1.86 (con)
% 7.83/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (line_connecting(v1,
% 7.83/1.87 v0) = v3 & line_connecting(v0, v1) = v2 & distinct_lines(v2, v3) = 0 &
% 7.83/1.87 distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.83/1.87
% 7.83/1.87 (con1)
% 7.83/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.83/1.87 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 7.83/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 7.83/1.87 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 7.83/1.87 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 7.83/1.87
% 7.83/1.87 (cu1)
% 7.83/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.83/1.87 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 7.83/1.87 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 7.83/1.87 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 7.83/1.87 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 7.83/1.87 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 7.83/1.87
% 7.83/1.87 (function-axioms)
% 7.83/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.83/1.88 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 7.83/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.83/1.88 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 7.83/1.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.83/1.88 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.83/1.88 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.83/1.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.83/1.88 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 7.83/1.88 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.83/1.88 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 7.83/1.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 7.83/1.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.83/1.88 (distinct_points(v3, v2) = v0))
% 7.83/1.88
% 7.83/1.88 Further assumptions not needed in the proof:
% 7.83/1.88 --------------------------------------------
% 7.83/1.88 apart2, apart3, apart5, apart6, ceq2, ceq3, con2
% 7.83/1.88
% 7.83/1.88 Those formulas are unsatisfiable:
% 7.83/1.88 ---------------------------------
% 7.83/1.88
% 7.83/1.88 Begin of proof
% 7.83/1.88 |
% 7.83/1.88 | ALPHA: (function-axioms) implies:
% 7.83/1.88 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.83/1.88 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.83/1.88 | (distinct_points(v3, v2) = v0))
% 7.83/1.88 |
% 7.83/1.88 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 7.83/1.88 | all_15_3 gives:
% 7.83/1.88 | (2) line_connecting(all_15_2, all_15_3) = all_15_0 &
% 7.83/1.88 | line_connecting(all_15_3, all_15_2) = all_15_1 &
% 7.83/1.88 | distinct_lines(all_15_1, all_15_0) = 0 & distinct_points(all_15_3,
% 7.83/1.88 | all_15_2) = 0 & $i(all_15_0) & $i(all_15_1) & $i(all_15_2) &
% 7.83/1.89 | $i(all_15_3)
% 7.83/1.89 |
% 7.83/1.89 | ALPHA: (2) implies:
% 7.83/1.89 | (3) $i(all_15_3)
% 7.83/1.89 | (4) $i(all_15_2)
% 7.83/1.89 | (5) $i(all_15_1)
% 7.83/1.89 | (6) $i(all_15_0)
% 7.83/1.89 | (7) distinct_points(all_15_3, all_15_2) = 0
% 7.83/1.89 | (8) distinct_lines(all_15_1, all_15_0) = 0
% 7.83/1.89 | (9) line_connecting(all_15_3, all_15_2) = all_15_1
% 8.28/1.89 | (10) line_connecting(all_15_2, all_15_3) = all_15_0
% 8.28/1.89 |
% 8.28/1.89 | GROUND_INST: instantiating (cu1) with all_15_3, all_15_2, all_15_1, all_15_0,
% 8.28/1.89 | simplifying with (3), (4), (5), (6), (7), (8) gives:
% 8.30/1.89 | (11) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 8.30/1.89 | (apart_point_and_line(all_15_2, all_15_0) = v3 &
% 8.30/1.89 | apart_point_and_line(all_15_2, all_15_1) = v2 &
% 8.30/1.89 | apart_point_and_line(all_15_3, all_15_0) = v1 &
% 8.30/1.89 | apart_point_and_line(all_15_3, all_15_1) = v0 & (v3 = 0 | v2 = 0 |
% 8.30/1.89 | v1 = 0 | v0 = 0))
% 8.30/1.89 |
% 8.30/1.89 | DELTA: instantiating (11) with fresh symbols all_22_0, all_22_1, all_22_2,
% 8.30/1.89 | all_22_3 gives:
% 8.30/1.89 | (12) apart_point_and_line(all_15_2, all_15_0) = all_22_0 &
% 8.30/1.89 | apart_point_and_line(all_15_2, all_15_1) = all_22_1 &
% 8.30/1.89 | apart_point_and_line(all_15_3, all_15_0) = all_22_2 &
% 8.30/1.89 | apart_point_and_line(all_15_3, all_15_1) = all_22_3 & (all_22_0 = 0 |
% 8.30/1.89 | all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0)
% 8.30/1.89 |
% 8.30/1.89 | ALPHA: (12) implies:
% 8.30/1.89 | (13) apart_point_and_line(all_15_3, all_15_1) = all_22_3
% 8.30/1.89 | (14) apart_point_and_line(all_15_3, all_15_0) = all_22_2
% 8.30/1.90 | (15) apart_point_and_line(all_15_2, all_15_1) = all_22_1
% 8.30/1.90 | (16) apart_point_and_line(all_15_2, all_15_0) = all_22_0
% 8.30/1.90 | (17) all_22_0 = 0 | all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0
% 8.30/1.90 |
% 8.30/1.90 | BETA: splitting (17) gives:
% 8.30/1.90 |
% 8.30/1.90 | Case 1:
% 8.30/1.90 | |
% 8.30/1.90 | | (18) all_22_0 = 0
% 8.30/1.90 | |
% 8.30/1.90 | | REDUCE: (16), (18) imply:
% 8.30/1.90 | | (19) apart_point_and_line(all_15_2, all_15_0) = 0
% 8.30/1.90 | |
% 8.30/1.90 | | GROUND_INST: instantiating (con1) with all_15_2, all_15_3, all_15_2,
% 8.30/1.90 | | all_15_0, simplifying with (3), (4), (10), (19) gives:
% 8.30/1.90 | | (20) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.30/1.90 | | (distinct_points(all_15_2, all_15_2) = v1 &
% 8.30/1.90 | | distinct_points(all_15_2, all_15_3) = v2 &
% 8.30/1.90 | | distinct_points(all_15_2, all_15_3) = v0 & ( ~ (v0 = 0) | (v2 = 0
% 8.30/1.90 | | & v1 = 0)))
% 8.34/1.90 | |
% 8.34/1.90 | | DELTA: instantiating (20) with fresh symbols all_36_0, all_36_1, all_36_2
% 8.34/1.90 | | gives:
% 8.34/1.90 | | (21) distinct_points(all_15_2, all_15_2) = all_36_1 &
% 8.34/1.90 | | distinct_points(all_15_2, all_15_3) = all_36_0 &
% 8.34/1.90 | | distinct_points(all_15_2, all_15_3) = all_36_2 & ( ~ (all_36_2 = 0)
% 8.34/1.90 | | | (all_36_0 = 0 & all_36_1 = 0))
% 8.34/1.90 | |
% 8.34/1.90 | | ALPHA: (21) implies:
% 8.34/1.90 | | (22) distinct_points(all_15_2, all_15_3) = all_36_2
% 8.34/1.90 | | (23) distinct_points(all_15_2, all_15_3) = all_36_0
% 8.34/1.90 | | (24) distinct_points(all_15_2, all_15_2) = all_36_1
% 8.34/1.90 | | (25) ~ (all_36_2 = 0) | (all_36_0 = 0 & all_36_1 = 0)
% 8.34/1.90 | |
% 8.34/1.90 | | GROUND_INST: instantiating (1) with all_36_2, all_36_0, all_15_3, all_15_2,
% 8.34/1.90 | | simplifying with (22), (23) gives:
% 8.34/1.90 | | (26) all_36_0 = all_36_2
% 8.34/1.90 | |
% 8.34/1.90 | | GROUND_INST: instantiating (ceq1) with all_15_2, all_15_0, all_15_3,
% 8.34/1.90 | | all_36_2, simplifying with (3), (4), (6), (19), (22) gives:
% 8.36/1.90 | | (27) all_36_2 = 0 | apart_point_and_line(all_15_3, all_15_0) = 0
% 8.36/1.90 | |
% 8.36/1.90 | | BETA: splitting (25) gives:
% 8.36/1.90 | |
% 8.36/1.90 | | Case 1:
% 8.36/1.90 | | |
% 8.36/1.91 | | | (28) ~ (all_36_2 = 0)
% 8.36/1.91 | | |
% 8.36/1.91 | | | BETA: splitting (27) gives:
% 8.36/1.91 | | |
% 8.36/1.91 | | | Case 1:
% 8.36/1.91 | | | |
% 8.36/1.91 | | | | (29) apart_point_and_line(all_15_3, all_15_0) = 0
% 8.36/1.91 | | | |
% 8.36/1.91 | | | | REF_CLOSE: (1), (3), (4), (7), (10), (29), (apart1), (apart4), (con1)
% 8.36/1.91 | | | | are inconsistent by sub-proof #1.
% 8.36/1.91 | | | |
% 8.36/1.91 | | | Case 2:
% 8.36/1.91 | | | |
% 8.36/1.91 | | | | (30) all_36_2 = 0
% 8.36/1.91 | | | |
% 8.36/1.91 | | | | REDUCE: (28), (30) imply:
% 8.36/1.91 | | | | (31) $false
% 8.36/1.91 | | | |
% 8.36/1.91 | | | | CLOSE: (31) is inconsistent.
% 8.36/1.91 | | | |
% 8.36/1.91 | | | End of split
% 8.36/1.91 | | |
% 8.36/1.91 | | Case 2:
% 8.36/1.91 | | |
% 8.36/1.91 | | | (32) all_36_0 = 0 & all_36_1 = 0
% 8.36/1.91 | | |
% 8.36/1.91 | | | ALPHA: (32) implies:
% 8.36/1.91 | | | (33) all_36_1 = 0
% 8.36/1.91 | | |
% 8.36/1.91 | | | REDUCE: (24), (33) imply:
% 8.36/1.91 | | | (34) distinct_points(all_15_2, all_15_2) = 0
% 8.36/1.91 | | |
% 8.36/1.91 | | | GROUND_INST: instantiating (apart1) with all_15_2, simplifying with (4),
% 8.36/1.91 | | | (34) gives:
% 8.36/1.91 | | | (35) $false
% 8.36/1.91 | | |
% 8.36/1.91 | | | CLOSE: (35) is inconsistent.
% 8.36/1.91 | | |
% 8.36/1.91 | | End of split
% 8.36/1.91 | |
% 8.36/1.91 | Case 2:
% 8.36/1.91 | |
% 8.36/1.91 | | (36) all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0
% 8.36/1.91 | |
% 8.36/1.91 | | BETA: splitting (36) gives:
% 8.36/1.91 | |
% 8.36/1.91 | | Case 1:
% 8.36/1.91 | | |
% 8.36/1.91 | | | (37) all_22_1 = 0
% 8.36/1.91 | | |
% 8.36/1.91 | | | REDUCE: (15), (37) imply:
% 8.36/1.91 | | | (38) apart_point_and_line(all_15_2, all_15_1) = 0
% 8.36/1.91 | | |
% 8.36/1.91 | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_2, all_15_2,
% 8.36/1.91 | | | all_15_1, simplifying with (3), (4), (9), (38) gives:
% 8.36/1.91 | | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.36/1.91 | | | (distinct_points(all_15_2, all_15_2) = v2 &
% 8.36/1.91 | | | distinct_points(all_15_2, all_15_3) = v1 &
% 8.36/1.91 | | | distinct_points(all_15_3, all_15_2) = v0 & ( ~ (v0 = 0) | (v2 =
% 8.36/1.91 | | | 0 & v1 = 0)))
% 8.36/1.91 | | |
% 8.36/1.91 | | | DELTA: instantiating (39) with fresh symbols all_43_0, all_43_1, all_43_2
% 8.36/1.91 | | | gives:
% 8.36/1.92 | | | (40) distinct_points(all_15_2, all_15_2) = all_43_0 &
% 8.36/1.92 | | | distinct_points(all_15_2, all_15_3) = all_43_1 &
% 8.36/1.92 | | | distinct_points(all_15_3, all_15_2) = all_43_2 & ( ~ (all_43_2 =
% 8.36/1.92 | | | 0) | (all_43_0 = 0 & all_43_1 = 0))
% 8.36/1.92 | | |
% 8.36/1.92 | | | ALPHA: (40) implies:
% 8.36/1.92 | | | (41) distinct_points(all_15_3, all_15_2) = all_43_2
% 8.36/1.92 | | | (42) distinct_points(all_15_2, all_15_2) = all_43_0
% 8.36/1.92 | | | (43) ~ (all_43_2 = 0) | (all_43_0 = 0 & all_43_1 = 0)
% 8.36/1.92 | | |
% 8.36/1.92 | | | GROUND_INST: instantiating (1) with 0, all_43_2, all_15_2, all_15_3,
% 8.36/1.92 | | | simplifying with (7), (41) gives:
% 8.36/1.92 | | | (44) all_43_2 = 0
% 8.36/1.92 | | |
% 8.36/1.92 | | | BETA: splitting (43) gives:
% 8.36/1.92 | | |
% 8.36/1.92 | | | Case 1:
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | (45) ~ (all_43_2 = 0)
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | REDUCE: (44), (45) imply:
% 8.36/1.92 | | | | (46) $false
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | CLOSE: (46) is inconsistent.
% 8.36/1.92 | | | |
% 8.36/1.92 | | | Case 2:
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | (47) all_43_0 = 0 & all_43_1 = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | ALPHA: (47) implies:
% 8.36/1.92 | | | | (48) all_43_0 = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | REDUCE: (42), (48) imply:
% 8.36/1.92 | | | | (49) distinct_points(all_15_2, all_15_2) = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | GROUND_INST: instantiating (apart1) with all_15_2, simplifying with (4),
% 8.36/1.92 | | | | (49) gives:
% 8.36/1.92 | | | | (50) $false
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | CLOSE: (50) is inconsistent.
% 8.36/1.92 | | | |
% 8.36/1.92 | | | End of split
% 8.36/1.92 | | |
% 8.36/1.92 | | Case 2:
% 8.36/1.92 | | |
% 8.36/1.92 | | | (51) all_22_2 = 0 | all_22_3 = 0
% 8.36/1.92 | | |
% 8.36/1.92 | | | BETA: splitting (51) gives:
% 8.36/1.92 | | |
% 8.36/1.92 | | | Case 1:
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | (52) all_22_2 = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | REDUCE: (14), (52) imply:
% 8.36/1.92 | | | | (53) apart_point_and_line(all_15_3, all_15_0) = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | REF_CLOSE: (1), (3), (4), (7), (10), (53), (apart1), (apart4), (con1)
% 8.36/1.92 | | | | are inconsistent by sub-proof #1.
% 8.36/1.92 | | | |
% 8.36/1.92 | | | Case 2:
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | (54) all_22_3 = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | REDUCE: (13), (54) imply:
% 8.36/1.92 | | | | (55) apart_point_and_line(all_15_3, all_15_1) = 0
% 8.36/1.92 | | | |
% 8.36/1.92 | | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_2, all_15_3,
% 8.36/1.92 | | | | all_15_1, simplifying with (3), (4), (9), (55) gives:
% 8.36/1.92 | | | | (56) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.36/1.92 | | | | (distinct_points(all_15_3, all_15_2) = v2 &
% 8.36/1.92 | | | | distinct_points(all_15_3, all_15_2) = v0 &
% 8.36/1.92 | | | | distinct_points(all_15_3, all_15_3) = v1 & ( ~ (v0 = 0) | (v2
% 8.36/1.93 | | | | = 0 & v1 = 0)))
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | DELTA: instantiating (56) with fresh symbols all_50_0, all_50_1,
% 8.36/1.93 | | | | all_50_2 gives:
% 8.36/1.93 | | | | (57) distinct_points(all_15_3, all_15_2) = all_50_0 &
% 8.36/1.93 | | | | distinct_points(all_15_3, all_15_2) = all_50_2 &
% 8.36/1.93 | | | | distinct_points(all_15_3, all_15_3) = all_50_1 & ( ~ (all_50_2 =
% 8.36/1.93 | | | | 0) | (all_50_0 = 0 & all_50_1 = 0))
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | ALPHA: (57) implies:
% 8.36/1.93 | | | | (58) distinct_points(all_15_3, all_15_3) = all_50_1
% 8.36/1.93 | | | | (59) distinct_points(all_15_3, all_15_2) = all_50_2
% 8.36/1.93 | | | | (60) distinct_points(all_15_3, all_15_2) = all_50_0
% 8.36/1.93 | | | | (61) ~ (all_50_2 = 0) | (all_50_0 = 0 & all_50_1 = 0)
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | GROUND_INST: instantiating (1) with 0, all_50_0, all_15_2, all_15_3,
% 8.36/1.93 | | | | simplifying with (7), (60) gives:
% 8.36/1.93 | | | | (62) all_50_0 = 0
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | GROUND_INST: instantiating (1) with all_50_2, all_50_0, all_15_2,
% 8.36/1.93 | | | | all_15_3, simplifying with (59), (60) gives:
% 8.36/1.93 | | | | (63) all_50_0 = all_50_2
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | COMBINE_EQS: (62), (63) imply:
% 8.36/1.93 | | | | (64) all_50_2 = 0
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | BETA: splitting (61) gives:
% 8.36/1.93 | | | |
% 8.36/1.93 | | | | Case 1:
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | (65) ~ (all_50_2 = 0)
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | REDUCE: (64), (65) imply:
% 8.36/1.93 | | | | | (66) $false
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | CLOSE: (66) is inconsistent.
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | Case 2:
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | (67) all_50_0 = 0 & all_50_1 = 0
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | ALPHA: (67) implies:
% 8.36/1.93 | | | | | (68) all_50_1 = 0
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | REDUCE: (58), (68) imply:
% 8.36/1.93 | | | | | (69) distinct_points(all_15_3, all_15_3) = 0
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | GROUND_INST: instantiating (apart1) with all_15_3, simplifying with
% 8.36/1.93 | | | | | (3), (69) gives:
% 8.36/1.93 | | | | | (70) $false
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | | CLOSE: (70) is inconsistent.
% 8.36/1.93 | | | | |
% 8.36/1.93 | | | | End of split
% 8.36/1.93 | | | |
% 8.36/1.93 | | | End of split
% 8.36/1.93 | | |
% 8.36/1.93 | | End of split
% 8.36/1.93 | |
% 8.36/1.93 | End of split
% 8.36/1.93 |
% 8.36/1.93 End of proof
% 8.36/1.93
% 8.36/1.93 Sub-proof #1 shows that the following formulas are inconsistent:
% 8.36/1.93 ----------------------------------------------------------------
% 8.36/1.93 (1) $i(all_15_2)
% 8.36/1.93 (2) line_connecting(all_15_2, all_15_3) = all_15_0
% 8.36/1.93 (3) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 8.36/1.93 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.36/1.93 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 8.36/1.93 (distinct_points(v3, v2) = v0))
% 8.36/1.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 8.36/1.94 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0)
% 8.36/1.94 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 8.36/1.94 [v6: any] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) =
% 8.36/1.94 v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 =
% 8.36/1.94 0))))
% 8.36/1.94 (6) distinct_points(all_15_3, all_15_2) = 0
% 8.36/1.94 (7) $i(all_15_3)
% 8.36/1.94 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.36/1.94 (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | ~
% 8.36/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v1, v2) = 0)
% 8.36/1.94 (9) apart_point_and_line(all_15_3, all_15_0) = 0
% 8.36/1.94
% 8.36/1.94 Begin of proof
% 8.36/1.94 |
% 8.36/1.94 | GROUND_INST: instantiating (5) with all_15_2, all_15_3, all_15_3, all_15_0,
% 8.36/1.94 | simplifying with (1), (2), (7), (9) gives:
% 8.36/1.94 | (10) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 8.36/1.94 | (distinct_points(all_15_2, all_15_3) = v0 & distinct_points(all_15_3,
% 8.36/1.94 | all_15_2) = v1 & distinct_points(all_15_3, all_15_3) = v2 & ( ~
% 8.36/1.94 | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 8.36/1.94 |
% 8.36/1.94 | DELTA: instantiating (10) with fresh symbols all_50_0, all_50_1, all_50_2
% 8.36/1.94 | gives:
% 8.36/1.94 | (11) distinct_points(all_15_2, all_15_3) = all_50_2 &
% 8.36/1.94 | distinct_points(all_15_3, all_15_2) = all_50_1 &
% 8.36/1.94 | distinct_points(all_15_3, all_15_3) = all_50_0 & ( ~ (all_50_2 = 0) |
% 8.36/1.94 | (all_50_0 = 0 & all_50_1 = 0))
% 8.36/1.94 |
% 8.36/1.94 | ALPHA: (11) implies:
% 8.36/1.94 | (12) distinct_points(all_15_3, all_15_3) = all_50_0
% 8.36/1.94 | (13) distinct_points(all_15_3, all_15_2) = all_50_1
% 8.36/1.94 | (14) distinct_points(all_15_2, all_15_3) = all_50_2
% 8.36/1.94 | (15) ~ (all_50_2 = 0) | (all_50_0 = 0 & all_50_1 = 0)
% 8.36/1.94 |
% 8.36/1.94 | GROUND_INST: instantiating (4) with 0, all_50_1, all_15_2, all_15_3,
% 8.36/1.94 | simplifying with (6), (13) gives:
% 8.36/1.94 | (16) all_50_1 = 0
% 8.36/1.94 |
% 8.36/1.94 | GROUND_INST: instantiating (8) with all_15_3, all_15_2, all_15_3, all_50_0,
% 8.36/1.94 | simplifying with (1), (6), (7), (12) gives:
% 8.36/1.94 | (17) all_50_0 = 0 | distinct_points(all_15_2, all_15_3) = 0
% 8.36/1.94 |
% 8.36/1.94 | BETA: splitting (15) gives:
% 8.36/1.94 |
% 8.36/1.94 | Case 1:
% 8.36/1.94 | |
% 8.36/1.94 | | (18) ~ (all_50_2 = 0)
% 8.36/1.94 | |
% 8.36/1.94 | | BETA: splitting (17) gives:
% 8.36/1.94 | |
% 8.36/1.94 | | Case 1:
% 8.36/1.94 | | |
% 8.36/1.94 | | | (19) distinct_points(all_15_2, all_15_3) = 0
% 8.36/1.94 | | |
% 8.36/1.94 | | | GROUND_INST: instantiating (4) with all_50_2, 0, all_15_3, all_15_2,
% 8.36/1.94 | | | simplifying with (14), (19) gives:
% 8.36/1.94 | | | (20) all_50_2 = 0
% 8.36/1.94 | | |
% 8.36/1.94 | | | REDUCE: (18), (20) imply:
% 8.36/1.94 | | | (21) $false
% 8.36/1.94 | | |
% 8.36/1.94 | | | CLOSE: (21) is inconsistent.
% 8.36/1.94 | | |
% 8.36/1.94 | | Case 2:
% 8.36/1.94 | | |
% 8.36/1.94 | | | (22) all_50_0 = 0
% 8.36/1.95 | | |
% 8.36/1.95 | | | REDUCE: (12), (22) imply:
% 8.36/1.95 | | | (23) distinct_points(all_15_3, all_15_3) = 0
% 8.36/1.95 | | |
% 8.36/1.95 | | | GROUND_INST: instantiating (3) with all_15_3, simplifying with (7), (23)
% 8.36/1.95 | | | gives:
% 8.36/1.95 | | | (24) $false
% 8.36/1.95 | | |
% 8.36/1.95 | | | CLOSE: (24) is inconsistent.
% 8.36/1.95 | | |
% 8.36/1.95 | | End of split
% 8.36/1.95 | |
% 8.36/1.95 | Case 2:
% 8.36/1.95 | |
% 8.36/1.95 | | (25) all_50_0 = 0 & all_50_1 = 0
% 8.36/1.95 | |
% 8.36/1.95 | | ALPHA: (25) implies:
% 8.36/1.95 | | (26) all_50_0 = 0
% 8.36/1.95 | |
% 8.36/1.95 | | REDUCE: (12), (26) imply:
% 8.36/1.95 | | (27) distinct_points(all_15_3, all_15_3) = 0
% 8.36/1.95 | |
% 8.36/1.95 | | GROUND_INST: instantiating (3) with all_15_3, simplifying with (7), (27)
% 8.36/1.95 | | gives:
% 8.36/1.95 | | (28) $false
% 8.36/1.95 | |
% 8.36/1.95 | | CLOSE: (28) is inconsistent.
% 8.36/1.95 | |
% 8.36/1.95 | End of split
% 8.36/1.95 |
% 8.36/1.95 End of proof
% 8.36/1.95 % SZS output end Proof for theBenchmark
% 8.36/1.95
% 8.36/1.95 1334ms
%------------------------------------------------------------------------------