TSTP Solution File: GEO185+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO185+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 23:21:59 EDT 2023

% Result   : Theorem 6.26s 1.64s
% Output   : Proof 9.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO185+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n018.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 : Wed Aug 30 00:10:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.66  ________       _____
% 0.18/0.66  ___  __ \_________(_)________________________________
% 0.18/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.66  
% 0.18/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.66  (2023-06-19)
% 0.18/0.66  
% 0.18/0.66  (c) Philipp Rümmer, 2009-2023
% 0.18/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.66                Amanda Stjerna.
% 0.18/0.66  Free software under BSD-3-Clause.
% 0.18/0.66  
% 0.18/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.66  
% 0.18/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.67  Running up to 7 provers in parallel.
% 0.18/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.30/1.14  Prover 1: Preprocessing ...
% 2.30/1.14  Prover 4: Preprocessing ...
% 3.06/1.20  Prover 6: Preprocessing ...
% 3.06/1.20  Prover 5: Preprocessing ...
% 3.06/1.20  Prover 3: Preprocessing ...
% 3.06/1.20  Prover 0: Preprocessing ...
% 3.06/1.20  Prover 2: Preprocessing ...
% 4.60/1.43  Prover 5: Proving ...
% 4.60/1.45  Prover 2: Proving ...
% 5.46/1.52  Prover 6: Constructing countermodel ...
% 5.46/1.53  Prover 1: Constructing countermodel ...
% 5.62/1.55  Prover 3: Constructing countermodel ...
% 6.26/1.63  Prover 3: proved (941ms)
% 6.26/1.63  
% 6.26/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.26/1.64  
% 6.26/1.64  Prover 2: stopped
% 6.26/1.64  Prover 5: stopped
% 6.26/1.64  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.26/1.64  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.26/1.64  Prover 6: stopped
% 6.26/1.65  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.26/1.65  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.73/1.70  Prover 7: Preprocessing ...
% 6.73/1.70  Prover 4: Constructing countermodel ...
% 6.73/1.72  Prover 8: Preprocessing ...
% 6.73/1.73  Prover 11: Preprocessing ...
% 6.73/1.73  Prover 10: Preprocessing ...
% 6.73/1.74  Prover 0: Proving ...
% 6.73/1.75  Prover 0: stopped
% 7.29/1.77  Prover 7: Warning: ignoring some quantifiers
% 7.29/1.77  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.36/1.78  Prover 7: Constructing countermodel ...
% 7.36/1.78  Prover 10: Warning: ignoring some quantifiers
% 7.36/1.80  Prover 10: Constructing countermodel ...
% 7.36/1.82  Prover 13: Preprocessing ...
% 7.36/1.85  Prover 8: Warning: ignoring some quantifiers
% 7.36/1.87  Prover 1: Found proof (size 35)
% 7.36/1.87  Prover 1: proved (1184ms)
% 7.36/1.87  Prover 10: stopped
% 7.36/1.87  Prover 4: stopped
% 7.36/1.87  Prover 7: stopped
% 7.36/1.87  Prover 8: Constructing countermodel ...
% 7.36/1.88  Prover 8: stopped
% 7.74/1.89  Prover 13: stopped
% 8.66/2.01  Prover 11: Constructing countermodel ...
% 8.66/2.02  Prover 11: stopped
% 8.66/2.02  
% 8.66/2.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.66/2.02  
% 8.66/2.03  % SZS output start Proof for theBenchmark
% 8.66/2.04  Assumptions after simplification:
% 8.66/2.04  ---------------------------------
% 8.66/2.04  
% 8.66/2.04    (con)
% 9.11/2.09     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 9.11/2.09      int] :  ? [v6: any] :  ? [v7: any] : ( ~ (v5 = 0) & intersection_point(v2,
% 9.11/2.09        v3) = v4 & apart_point_and_line(v0, v3) = v7 & apart_point_and_line(v0,
% 9.11/2.09        v2) = v6 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v4) = v5 &
% 9.11/2.09      distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 9.11/2.09      (v7 = 0 | v6 = 0))
% 9.11/2.09  
% 9.11/2.09    (con2)
% 9.11/2.09     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: int] : (v4 = 0
% 9.11/2.09      |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |
% 9.11/2.09       ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: any] :  ? [v6: any] :  ? [v7:
% 9.11/2.09        any] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) =
% 9.11/2.10        v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6
% 9.11/2.10              = 0)))))
% 9.11/2.10  
% 9.11/2.10    (function-axioms)
% 9.11/2.10     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.11/2.10      (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) & 
% 9.11/2.10    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.11/2.10      (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  !
% 9.11/2.10    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 9.11/2.10      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 9.11/2.10      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.11/2.10      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.11/2.10      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 9.11/2.10    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 9.11/2.10      $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3,
% 9.11/2.10          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 9.11/2.10    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 9.11/2.10      (distinct_points(v3, v2) = v0))
% 9.11/2.10  
% 9.11/2.10  Further assumptions not needed in the proof:
% 9.11/2.10  --------------------------------------------
% 9.11/2.11  apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con1, cu1
% 9.11/2.11  
% 9.11/2.11  Those formulas are unsatisfiable:
% 9.11/2.11  ---------------------------------
% 9.11/2.11  
% 9.11/2.11  Begin of proof
% 9.11/2.11  | 
% 9.11/2.11  | ALPHA: (function-axioms) implies:
% 9.11/2.11  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.11/2.11  |         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 9.11/2.11  |          (convergent_lines(v3, v2) = v0))
% 9.11/2.11  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.11/2.11  |         ! [v3: $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 9.11/2.11  |          (apart_point_and_line(v3, v2) = v0))
% 9.11/2.11  | 
% 9.11/2.11  | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 9.11/2.11  |        all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 9.11/2.12  |   (3)   ~ (all_15_2 = 0) & intersection_point(all_15_5, all_15_4) = all_15_3 &
% 9.11/2.12  |        apart_point_and_line(all_15_7, all_15_4) = all_15_0 &
% 9.11/2.12  |        apart_point_and_line(all_15_7, all_15_5) = all_15_1 &
% 9.11/2.12  |        convergent_lines(all_15_5, all_15_4) = 0 & distinct_points(all_15_7,
% 9.11/2.12  |          all_15_3) = all_15_2 & distinct_points(all_15_7, all_15_6) = 0 &
% 9.11/2.12  |        $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) &
% 9.11/2.12  |        $i(all_15_7) & (all_15_0 = 0 | all_15_1 = 0)
% 9.11/2.12  | 
% 9.11/2.12  | ALPHA: (3) implies:
% 9.11/2.12  |   (4)   ~ (all_15_2 = 0)
% 9.11/2.12  |   (5)  $i(all_15_7)
% 9.11/2.12  |   (6)  $i(all_15_5)
% 9.11/2.12  |   (7)  $i(all_15_4)
% 9.11/2.12  |   (8)  distinct_points(all_15_7, all_15_3) = all_15_2
% 9.11/2.12  |   (9)  convergent_lines(all_15_5, all_15_4) = 0
% 9.11/2.12  |   (10)  apart_point_and_line(all_15_7, all_15_5) = all_15_1
% 9.11/2.12  |   (11)  apart_point_and_line(all_15_7, all_15_4) = all_15_0
% 9.11/2.12  |   (12)  intersection_point(all_15_5, all_15_4) = all_15_3
% 9.11/2.12  |   (13)  all_15_0 = 0 | all_15_1 = 0
% 9.11/2.12  | 
% 9.11/2.12  | GROUND_INST: instantiating (con2) with all_15_5, all_15_4, all_15_7, all_15_3,
% 9.11/2.12  |              all_15_2, simplifying with (5), (6), (7), (8), (12) gives:
% 9.11/2.13  |   (14)  all_15_2 = 0 |  ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 9.11/2.13  |         (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 9.11/2.13  |           apart_point_and_line(all_15_7, all_15_5) = v1 &
% 9.11/2.13  |           convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~ (v2 =
% 9.11/2.13  |                 0) &  ~ (v1 = 0))))
% 9.11/2.13  | 
% 9.11/2.13  | BETA: splitting (13) gives:
% 9.11/2.13  | 
% 9.11/2.13  | Case 1:
% 9.11/2.13  | | 
% 9.11/2.13  | |   (15)  all_15_0 = 0
% 9.11/2.13  | | 
% 9.11/2.13  | | REDUCE: (11), (15) imply:
% 9.11/2.13  | |   (16)  apart_point_and_line(all_15_7, all_15_4) = 0
% 9.11/2.13  | | 
% 9.11/2.13  | | BETA: splitting (14) gives:
% 9.11/2.13  | | 
% 9.11/2.13  | | Case 1:
% 9.11/2.13  | | | 
% 9.11/2.13  | | |   (17)  all_15_2 = 0
% 9.11/2.13  | | | 
% 9.11/2.13  | | | REDUCE: (4), (17) imply:
% 9.11/2.13  | | |   (18)  $false
% 9.11/2.13  | | | 
% 9.11/2.13  | | | CLOSE: (18) is inconsistent.
% 9.11/2.13  | | | 
% 9.11/2.13  | | Case 2:
% 9.11/2.13  | | | 
% 9.11/2.13  | | |   (19)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 9.11/2.13  | | |         (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 9.11/2.13  | | |           apart_point_and_line(all_15_7, all_15_5) = v1 &
% 9.11/2.13  | | |           convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~
% 9.11/2.13  | | |               (v2 = 0) &  ~ (v1 = 0))))
% 9.11/2.13  | | | 
% 9.11/2.13  | | | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 9.11/2.13  | | |        gives:
% 9.11/2.14  | | |   (20)  apart_point_and_line(all_15_7, all_15_4) = all_32_0 &
% 9.11/2.14  | | |         apart_point_and_line(all_15_7, all_15_5) = all_32_1 &
% 9.11/2.14  | | |         convergent_lines(all_15_5, all_15_4) = all_32_2 & ( ~ (all_32_2 =
% 9.11/2.14  | | |             0) | ( ~ (all_32_0 = 0) &  ~ (all_32_1 = 0)))
% 9.11/2.14  | | | 
% 9.11/2.14  | | | ALPHA: (20) implies:
% 9.11/2.14  | | |   (21)  convergent_lines(all_15_5, all_15_4) = all_32_2
% 9.11/2.14  | | |   (22)  apart_point_and_line(all_15_7, all_15_4) = all_32_0
% 9.11/2.14  | | |   (23)   ~ (all_32_2 = 0) | ( ~ (all_32_0 = 0) &  ~ (all_32_1 = 0))
% 9.11/2.14  | | | 
% 9.11/2.14  | | | GROUND_INST: instantiating (1) with 0, all_32_2, all_15_4, all_15_5,
% 9.11/2.14  | | |              simplifying with (9), (21) gives:
% 9.11/2.14  | | |   (24)  all_32_2 = 0
% 9.11/2.14  | | | 
% 9.11/2.14  | | | GROUND_INST: instantiating (2) with 0, all_32_0, all_15_4, all_15_7,
% 9.11/2.14  | | |              simplifying with (16), (22) gives:
% 9.11/2.14  | | |   (25)  all_32_0 = 0
% 9.11/2.14  | | | 
% 9.11/2.14  | | | BETA: splitting (23) gives:
% 9.11/2.14  | | | 
% 9.11/2.14  | | | Case 1:
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | |   (26)   ~ (all_32_2 = 0)
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | | REDUCE: (24), (26) imply:
% 9.11/2.14  | | | |   (27)  $false
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | | CLOSE: (27) is inconsistent.
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | Case 2:
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | |   (28)   ~ (all_32_0 = 0) &  ~ (all_32_1 = 0)
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | | ALPHA: (28) implies:
% 9.11/2.14  | | | |   (29)   ~ (all_32_0 = 0)
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | | REDUCE: (25), (29) imply:
% 9.11/2.14  | | | |   (30)  $false
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | | CLOSE: (30) is inconsistent.
% 9.11/2.14  | | | | 
% 9.11/2.14  | | | End of split
% 9.11/2.14  | | | 
% 9.11/2.14  | | End of split
% 9.11/2.14  | | 
% 9.11/2.14  | Case 2:
% 9.11/2.14  | | 
% 9.11/2.14  | |   (31)  all_15_1 = 0
% 9.11/2.14  | | 
% 9.11/2.14  | | REDUCE: (10), (31) imply:
% 9.11/2.14  | |   (32)  apart_point_and_line(all_15_7, all_15_5) = 0
% 9.11/2.14  | | 
% 9.11/2.14  | | BETA: splitting (14) gives:
% 9.11/2.14  | | 
% 9.11/2.14  | | Case 1:
% 9.11/2.14  | | | 
% 9.11/2.14  | | |   (33)  all_15_2 = 0
% 9.11/2.14  | | | 
% 9.11/2.15  | | | REDUCE: (4), (33) imply:
% 9.11/2.15  | | |   (34)  $false
% 9.11/2.15  | | | 
% 9.11/2.15  | | | CLOSE: (34) is inconsistent.
% 9.11/2.15  | | | 
% 9.11/2.15  | | Case 2:
% 9.11/2.15  | | | 
% 9.11/2.15  | | |   (35)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 9.11/2.15  | | |         (apart_point_and_line(all_15_7, all_15_4) = v2 &
% 9.11/2.15  | | |           apart_point_and_line(all_15_7, all_15_5) = v1 &
% 9.11/2.15  | | |           convergent_lines(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | ( ~
% 9.11/2.15  | | |               (v2 = 0) &  ~ (v1 = 0))))
% 9.11/2.15  | | | 
% 9.11/2.15  | | | DELTA: instantiating (35) with fresh symbols all_32_0, all_32_1, all_32_2
% 9.11/2.15  | | |        gives:
% 9.11/2.15  | | |   (36)  apart_point_and_line(all_15_7, all_15_4) = all_32_0 &
% 9.11/2.15  | | |         apart_point_and_line(all_15_7, all_15_5) = all_32_1 &
% 9.11/2.15  | | |         convergent_lines(all_15_5, all_15_4) = all_32_2 & ( ~ (all_32_2 =
% 9.11/2.15  | | |             0) | ( ~ (all_32_0 = 0) &  ~ (all_32_1 = 0)))
% 9.11/2.15  | | | 
% 9.11/2.15  | | | ALPHA: (36) implies:
% 9.11/2.15  | | |   (37)  convergent_lines(all_15_5, all_15_4) = all_32_2
% 9.11/2.15  | | |   (38)  apart_point_and_line(all_15_7, all_15_5) = all_32_1
% 9.11/2.15  | | |   (39)   ~ (all_32_2 = 0) | ( ~ (all_32_0 = 0) &  ~ (all_32_1 = 0))
% 9.11/2.15  | | | 
% 9.11/2.15  | | | GROUND_INST: instantiating (1) with 0, all_32_2, all_15_4, all_15_5,
% 9.11/2.15  | | |              simplifying with (9), (37) gives:
% 9.11/2.15  | | |   (40)  all_32_2 = 0
% 9.11/2.15  | | | 
% 9.11/2.15  | | | GROUND_INST: instantiating (2) with 0, all_32_1, all_15_5, all_15_7,
% 9.11/2.15  | | |              simplifying with (32), (38) gives:
% 9.11/2.15  | | |   (41)  all_32_1 = 0
% 9.11/2.15  | | | 
% 9.11/2.15  | | | BETA: splitting (39) gives:
% 9.11/2.15  | | | 
% 9.11/2.15  | | | Case 1:
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | |   (42)   ~ (all_32_2 = 0)
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | | REDUCE: (40), (42) imply:
% 9.11/2.15  | | | |   (43)  $false
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | | CLOSE: (43) is inconsistent.
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | Case 2:
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | |   (44)   ~ (all_32_0 = 0) &  ~ (all_32_1 = 0)
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | | ALPHA: (44) implies:
% 9.11/2.15  | | | |   (45)   ~ (all_32_1 = 0)
% 9.11/2.15  | | | | 
% 9.11/2.15  | | | | REDUCE: (41), (45) imply:
% 9.11/2.15  | | | |   (46)  $false
% 9.11/2.16  | | | | 
% 9.11/2.16  | | | | CLOSE: (46) is inconsistent.
% 9.11/2.16  | | | | 
% 9.11/2.16  | | | End of split
% 9.11/2.16  | | | 
% 9.11/2.16  | | End of split
% 9.11/2.16  | | 
% 9.11/2.16  | End of split
% 9.11/2.16  | 
% 9.11/2.16  End of proof
% 9.11/2.16  % SZS output end Proof for theBenchmark
% 9.11/2.16  
% 9.11/2.16  1496ms
%------------------------------------------------------------------------------