TSTP Solution File: GEO173+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO173+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 : n016.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 23:21:50 EDT 2023
% Result : Theorem 6.09s 1.52s
% Output : Proof 7.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO173+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 22:09:01 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.61 Running up to 7 provers in parallel.
% 0.70/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.12/0.98 Prover 4: Preprocessing ...
% 2.12/0.99 Prover 1: Preprocessing ...
% 2.66/1.04 Prover 5: Preprocessing ...
% 2.66/1.04 Prover 6: Preprocessing ...
% 2.66/1.04 Prover 0: Preprocessing ...
% 2.66/1.04 Prover 3: Preprocessing ...
% 2.66/1.04 Prover 2: Preprocessing ...
% 4.22/1.27 Prover 5: Proving ...
% 4.22/1.29 Prover 3: Constructing countermodel ...
% 4.22/1.29 Prover 2: Proving ...
% 4.67/1.30 Prover 6: Constructing countermodel ...
% 4.67/1.31 Prover 1: Constructing countermodel ...
% 5.11/1.41 Prover 4: Constructing countermodel ...
% 5.11/1.44 Prover 0: Proving ...
% 6.09/1.52 Prover 6: proved (898ms)
% 6.09/1.52
% 6.09/1.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.09/1.52
% 6.09/1.52 Prover 3: stopped
% 6.09/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.09/1.53 Prover 0: stopped
% 6.38/1.54 Prover 5: proved (908ms)
% 6.38/1.54
% 6.38/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.38/1.54
% 6.38/1.54 Prover 2: proved (910ms)
% 6.38/1.54
% 6.38/1.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.38/1.54
% 6.38/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.38/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.38/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.38/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.38/1.56 Prover 7: Preprocessing ...
% 6.38/1.58 Prover 8: Preprocessing ...
% 6.38/1.58 Prover 11: Preprocessing ...
% 6.38/1.60 Prover 10: Preprocessing ...
% 6.38/1.60 Prover 13: Preprocessing ...
% 6.88/1.60 Prover 7: Warning: ignoring some quantifiers
% 6.88/1.61 Prover 7: Constructing countermodel ...
% 6.88/1.63 Prover 1: Found proof (size 44)
% 6.88/1.63 Prover 1: proved (1011ms)
% 6.88/1.63 Prover 7: stopped
% 6.88/1.63 Prover 4: stopped
% 6.88/1.64 Prover 11: stopped
% 6.88/1.64 Prover 10: Warning: ignoring some quantifiers
% 6.88/1.65 Prover 10: Constructing countermodel ...
% 6.88/1.65 Prover 13: Warning: ignoring some quantifiers
% 6.88/1.65 Prover 10: stopped
% 6.88/1.66 Prover 13: Constructing countermodel ...
% 6.88/1.66 Prover 13: stopped
% 6.88/1.67 Prover 8: Warning: ignoring some quantifiers
% 6.88/1.67 Prover 8: Constructing countermodel ...
% 6.88/1.67 Prover 8: stopped
% 6.88/1.67
% 6.88/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.88/1.67
% 7.39/1.68 % SZS output start Proof for theBenchmark
% 7.39/1.68 Assumptions after simplification:
% 7.39/1.68 ---------------------------------
% 7.39/1.68
% 7.39/1.69 (apart1)
% 7.39/1.71 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 7.39/1.71
% 7.39/1.71 (con)
% 7.39/1.71 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 7.39/1.71 int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v0, v1) =
% 7.39/1.71 v4 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v2) = v5 &
% 7.39/1.71 convergent_lines(v2, v3) = 0 & distinct_lines(v2, v4) = 0 &
% 7.39/1.71 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.39/1.71
% 7.39/1.71 (con1)
% 7.39/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.39/1.71 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 7.39/1.71 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 7.39/1.71 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 7.39/1.71 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 7.39/1.71
% 7.39/1.72 (cu1)
% 7.39/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 7.39/1.72 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 7.39/1.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 7.39/1.72 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 7.39/1.72 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 7.39/1.72 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 7.39/1.72
% 7.39/1.72 (function-axioms)
% 7.39/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.39/1.72 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 7.39/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.39/1.72 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 7.39/1.72 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.39/1.72 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.39/1.72 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.39/1.72 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.39/1.72 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 7.39/1.72 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.39/1.72 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 7.39/1.72 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 7.39/1.72 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.39/1.72 (distinct_points(v3, v2) = v0))
% 7.39/1.72
% 7.39/1.72 Further assumptions not needed in the proof:
% 7.39/1.72 --------------------------------------------
% 7.39/1.72 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con2
% 7.39/1.72
% 7.39/1.72 Those formulas are unsatisfiable:
% 7.39/1.72 ---------------------------------
% 7.39/1.72
% 7.39/1.72 Begin of proof
% 7.39/1.73 |
% 7.39/1.73 | ALPHA: (function-axioms) implies:
% 7.39/1.73 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.39/1.73 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 7.39/1.73 | (distinct_points(v3, v2) = v0))
% 7.39/1.73 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.39/1.73 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 7.39/1.73 | (apart_point_and_line(v3, v2) = v0))
% 7.39/1.73 |
% 7.39/1.73 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 7.39/1.73 | all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 7.39/1.73 | (3) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & line_connecting(all_15_6,
% 7.39/1.73 | all_15_5) = all_15_2 & apart_point_and_line(all_15_5, all_15_4) =
% 7.39/1.73 | all_15_0 & apart_point_and_line(all_15_6, all_15_4) = all_15_1 &
% 7.39/1.73 | convergent_lines(all_15_4, all_15_3) = 0 & distinct_lines(all_15_4,
% 7.39/1.73 | all_15_2) = 0 & distinct_points(all_15_6, all_15_5) = 0 &
% 7.39/1.73 | $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & $i(all_15_5) &
% 7.39/1.73 | $i(all_15_6)
% 7.39/1.73 |
% 7.39/1.73 | ALPHA: (3) implies:
% 7.39/1.73 | (4) ~ (all_15_1 = 0)
% 7.39/1.73 | (5) ~ (all_15_0 = 0)
% 7.39/1.73 | (6) $i(all_15_6)
% 7.39/1.73 | (7) $i(all_15_5)
% 7.39/1.73 | (8) $i(all_15_4)
% 7.39/1.73 | (9) $i(all_15_2)
% 7.39/1.73 | (10) distinct_points(all_15_6, all_15_5) = 0
% 7.39/1.73 | (11) distinct_lines(all_15_4, all_15_2) = 0
% 7.39/1.73 | (12) apart_point_and_line(all_15_6, all_15_4) = all_15_1
% 7.39/1.74 | (13) apart_point_and_line(all_15_5, all_15_4) = all_15_0
% 7.39/1.74 | (14) line_connecting(all_15_6, all_15_5) = all_15_2
% 7.39/1.74 |
% 7.39/1.74 | GROUND_INST: instantiating (cu1) with all_15_6, all_15_5, all_15_4, all_15_2,
% 7.39/1.74 | simplifying with (6), (7), (8), (9), (10), (11) gives:
% 7.39/1.74 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 7.39/1.74 | (apart_point_and_line(all_15_5, all_15_2) = v3 &
% 7.39/1.74 | apart_point_and_line(all_15_5, all_15_4) = v2 &
% 7.39/1.74 | apart_point_and_line(all_15_6, all_15_2) = v1 &
% 7.39/1.74 | apart_point_and_line(all_15_6, all_15_4) = v0 & (v3 = 0 | v2 = 0 |
% 7.39/1.74 | v1 = 0 | v0 = 0))
% 7.39/1.74 |
% 7.39/1.74 | DELTA: instantiating (15) with fresh symbols all_23_0, all_23_1, all_23_2,
% 7.39/1.74 | all_23_3 gives:
% 7.39/1.74 | (16) apart_point_and_line(all_15_5, all_15_2) = all_23_0 &
% 7.39/1.74 | apart_point_and_line(all_15_5, all_15_4) = all_23_1 &
% 7.39/1.74 | apart_point_and_line(all_15_6, all_15_2) = all_23_2 &
% 7.39/1.74 | apart_point_and_line(all_15_6, all_15_4) = all_23_3 & (all_23_0 = 0 |
% 7.39/1.74 | all_23_1 = 0 | all_23_2 = 0 | all_23_3 = 0)
% 7.39/1.74 |
% 7.39/1.74 | ALPHA: (16) implies:
% 7.39/1.74 | (17) apart_point_and_line(all_15_6, all_15_4) = all_23_3
% 7.39/1.74 | (18) apart_point_and_line(all_15_6, all_15_2) = all_23_2
% 7.39/1.74 | (19) apart_point_and_line(all_15_5, all_15_4) = all_23_1
% 7.39/1.74 | (20) apart_point_and_line(all_15_5, all_15_2) = all_23_0
% 7.39/1.74 | (21) all_23_0 = 0 | all_23_1 = 0 | all_23_2 = 0 | all_23_3 = 0
% 7.39/1.74 |
% 7.39/1.74 | GROUND_INST: instantiating (2) with all_15_1, all_23_3, all_15_4, all_15_6,
% 7.39/1.74 | simplifying with (12), (17) gives:
% 7.39/1.74 | (22) all_23_3 = all_15_1
% 7.39/1.74 |
% 7.39/1.74 | GROUND_INST: instantiating (2) with all_15_0, all_23_1, all_15_4, all_15_5,
% 7.39/1.74 | simplifying with (13), (19) gives:
% 7.39/1.74 | (23) all_23_1 = all_15_0
% 7.39/1.74 |
% 7.39/1.74 | BETA: splitting (21) gives:
% 7.39/1.74 |
% 7.39/1.74 | Case 1:
% 7.39/1.74 | |
% 7.39/1.74 | | (24) all_23_0 = 0
% 7.39/1.74 | |
% 7.39/1.74 | | REDUCE: (20), (24) imply:
% 7.39/1.74 | | (25) apart_point_and_line(all_15_5, all_15_2) = 0
% 7.39/1.74 | |
% 7.39/1.74 | | GROUND_INST: instantiating (con1) with all_15_6, all_15_5, all_15_5,
% 7.39/1.74 | | all_15_2, simplifying with (6), (7), (14), (25) gives:
% 7.39/1.74 | | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 7.39/1.74 | | (distinct_points(all_15_5, all_15_5) = v2 &
% 7.39/1.74 | | distinct_points(all_15_5, all_15_6) = v1 &
% 7.39/1.74 | | distinct_points(all_15_6, all_15_5) = v0 & ( ~ (v0 = 0) | (v2 = 0
% 7.39/1.75 | | & v1 = 0)))
% 7.39/1.75 | |
% 7.39/1.75 | | DELTA: instantiating (26) with fresh symbols all_52_0, all_52_1, all_52_2
% 7.39/1.75 | | gives:
% 7.39/1.75 | | (27) distinct_points(all_15_5, all_15_5) = all_52_0 &
% 7.39/1.75 | | distinct_points(all_15_5, all_15_6) = all_52_1 &
% 7.39/1.75 | | distinct_points(all_15_6, all_15_5) = all_52_2 & ( ~ (all_52_2 = 0)
% 7.39/1.75 | | | (all_52_0 = 0 & all_52_1 = 0))
% 7.39/1.75 | |
% 7.39/1.75 | | ALPHA: (27) implies:
% 7.39/1.75 | | (28) distinct_points(all_15_6, all_15_5) = all_52_2
% 7.39/1.75 | | (29) distinct_points(all_15_5, all_15_5) = all_52_0
% 7.39/1.75 | | (30) ~ (all_52_2 = 0) | (all_52_0 = 0 & all_52_1 = 0)
% 7.39/1.75 | |
% 7.39/1.75 | | GROUND_INST: instantiating (1) with 0, all_52_2, all_15_5, all_15_6,
% 7.39/1.75 | | simplifying with (10), (28) gives:
% 7.39/1.75 | | (31) all_52_2 = 0
% 7.39/1.75 | |
% 7.39/1.75 | | BETA: splitting (30) gives:
% 7.39/1.75 | |
% 7.39/1.75 | | Case 1:
% 7.39/1.75 | | |
% 7.39/1.75 | | | (32) ~ (all_52_2 = 0)
% 7.39/1.75 | | |
% 7.39/1.75 | | | REDUCE: (31), (32) imply:
% 7.39/1.75 | | | (33) $false
% 7.39/1.75 | | |
% 7.39/1.75 | | | CLOSE: (33) is inconsistent.
% 7.39/1.75 | | |
% 7.39/1.75 | | Case 2:
% 7.39/1.75 | | |
% 7.39/1.75 | | | (34) all_52_0 = 0 & all_52_1 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | ALPHA: (34) implies:
% 7.39/1.75 | | | (35) all_52_0 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | REDUCE: (29), (35) imply:
% 7.39/1.75 | | | (36) distinct_points(all_15_5, all_15_5) = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with (7),
% 7.39/1.75 | | | (36) gives:
% 7.39/1.75 | | | (37) $false
% 7.39/1.75 | | |
% 7.39/1.75 | | | CLOSE: (37) is inconsistent.
% 7.39/1.75 | | |
% 7.39/1.75 | | End of split
% 7.39/1.75 | |
% 7.39/1.75 | Case 2:
% 7.39/1.75 | |
% 7.39/1.75 | | (38) all_23_1 = 0 | all_23_2 = 0 | all_23_3 = 0
% 7.39/1.75 | |
% 7.39/1.75 | | BETA: splitting (38) gives:
% 7.39/1.75 | |
% 7.39/1.75 | | Case 1:
% 7.39/1.75 | | |
% 7.39/1.75 | | | (39) all_23_1 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | COMBINE_EQS: (23), (39) imply:
% 7.39/1.75 | | | (40) all_15_0 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | SIMP: (40) implies:
% 7.39/1.75 | | | (41) all_15_0 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | REDUCE: (5), (41) imply:
% 7.39/1.75 | | | (42) $false
% 7.39/1.75 | | |
% 7.39/1.75 | | | CLOSE: (42) is inconsistent.
% 7.39/1.75 | | |
% 7.39/1.75 | | Case 2:
% 7.39/1.75 | | |
% 7.39/1.75 | | | (43) all_23_2 = 0 | all_23_3 = 0
% 7.39/1.75 | | |
% 7.39/1.75 | | | BETA: splitting (43) gives:
% 7.39/1.75 | | |
% 7.39/1.75 | | | Case 1:
% 7.39/1.75 | | | |
% 7.39/1.75 | | | | (44) all_23_2 = 0
% 7.39/1.75 | | | |
% 7.39/1.75 | | | | REDUCE: (18), (44) imply:
% 7.39/1.75 | | | | (45) apart_point_and_line(all_15_6, all_15_2) = 0
% 7.39/1.75 | | | |
% 7.39/1.75 | | | | GROUND_INST: instantiating (con1) with all_15_6, all_15_5, all_15_6,
% 7.39/1.75 | | | | all_15_2, simplifying with (6), (7), (14), (45) gives:
% 7.39/1.75 | | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 7.39/1.75 | | | | (distinct_points(all_15_6, all_15_5) = v2 &
% 7.39/1.75 | | | | distinct_points(all_15_6, all_15_5) = v0 &
% 7.39/1.75 | | | | distinct_points(all_15_6, all_15_6) = v1 & ( ~ (v0 = 0) | (v2
% 7.39/1.75 | | | | = 0 & v1 = 0)))
% 7.39/1.75 | | | |
% 7.39/1.75 | | | | DELTA: instantiating (46) with fresh symbols all_60_0, all_60_1,
% 7.39/1.75 | | | | all_60_2 gives:
% 7.39/1.75 | | | | (47) distinct_points(all_15_6, all_15_5) = all_60_0 &
% 7.39/1.75 | | | | distinct_points(all_15_6, all_15_5) = all_60_2 &
% 7.39/1.75 | | | | distinct_points(all_15_6, all_15_6) = all_60_1 & ( ~ (all_60_2 =
% 7.39/1.75 | | | | 0) | (all_60_0 = 0 & all_60_1 = 0))
% 7.39/1.75 | | | |
% 7.39/1.75 | | | | ALPHA: (47) implies:
% 7.39/1.76 | | | | (48) distinct_points(all_15_6, all_15_6) = all_60_1
% 7.39/1.76 | | | | (49) distinct_points(all_15_6, all_15_5) = all_60_2
% 7.39/1.76 | | | | (50) distinct_points(all_15_6, all_15_5) = all_60_0
% 7.39/1.76 | | | | (51) ~ (all_60_2 = 0) | (all_60_0 = 0 & all_60_1 = 0)
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | GROUND_INST: instantiating (1) with 0, all_60_0, all_15_5, all_15_6,
% 7.39/1.76 | | | | simplifying with (10), (50) gives:
% 7.39/1.76 | | | | (52) all_60_0 = 0
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | GROUND_INST: instantiating (1) with all_60_2, all_60_0, all_15_5,
% 7.39/1.76 | | | | all_15_6, simplifying with (49), (50) gives:
% 7.39/1.76 | | | | (53) all_60_0 = all_60_2
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | COMBINE_EQS: (52), (53) imply:
% 7.39/1.76 | | | | (54) all_60_2 = 0
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | BETA: splitting (51) gives:
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | Case 1:
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | (55) ~ (all_60_2 = 0)
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | REDUCE: (54), (55) imply:
% 7.39/1.76 | | | | | (56) $false
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | CLOSE: (56) is inconsistent.
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | Case 2:
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | (57) all_60_0 = 0 & all_60_1 = 0
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | ALPHA: (57) implies:
% 7.39/1.76 | | | | | (58) all_60_1 = 0
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | REDUCE: (48), (58) imply:
% 7.39/1.76 | | | | | (59) distinct_points(all_15_6, all_15_6) = 0
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | GROUND_INST: instantiating (apart1) with all_15_6, simplifying with
% 7.39/1.76 | | | | | (6), (59) gives:
% 7.39/1.76 | | | | | (60) $false
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | | CLOSE: (60) is inconsistent.
% 7.39/1.76 | | | | |
% 7.39/1.76 | | | | End of split
% 7.39/1.76 | | | |
% 7.39/1.76 | | | Case 2:
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | (61) all_23_3 = 0
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | COMBINE_EQS: (22), (61) imply:
% 7.39/1.76 | | | | (62) all_15_1 = 0
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | REDUCE: (4), (62) imply:
% 7.39/1.76 | | | | (63) $false
% 7.39/1.76 | | | |
% 7.39/1.76 | | | | CLOSE: (63) is inconsistent.
% 7.39/1.76 | | | |
% 7.39/1.76 | | | End of split
% 7.39/1.76 | | |
% 7.39/1.76 | | End of split
% 7.39/1.76 | |
% 7.39/1.76 | End of split
% 7.39/1.76 |
% 7.39/1.76 End of proof
% 7.39/1.76 % SZS output end Proof for theBenchmark
% 7.39/1.76
% 7.39/1.76 1163ms
%------------------------------------------------------------------------------