TSTP Solution File: GEO173+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO173+3 : TPTP v8.1.2. Released v4.0.0.
% 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 23:21:50 EDT 2023

% Result   : Theorem 7.60s 1.86s
% Output   : Proof 10.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO173+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n018.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 22:42:03 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.65  ________       _____
% 0.20/0.65  ___  __ \_________(_)________________________________
% 0.20/0.65  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.65  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.65  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65  
% 0.20/0.65  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65  (2023-06-19)
% 0.20/0.65  
% 0.20/0.65  (c) Philipp Rümmer, 2009-2023
% 0.20/0.65  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65                Amanda Stjerna.
% 0.20/0.65  Free software under BSD-3-Clause.
% 0.20/0.65  
% 0.20/0.65  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65  
% 0.20/0.65  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.67  Running up to 7 provers in parallel.
% 0.86/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.86/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.86/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.86/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.86/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.86/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.86/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.23/1.21  Prover 1: Preprocessing ...
% 3.23/1.22  Prover 4: Preprocessing ...
% 3.23/1.25  Prover 6: Preprocessing ...
% 3.23/1.25  Prover 2: Preprocessing ...
% 3.23/1.25  Prover 5: Preprocessing ...
% 3.23/1.26  Prover 3: Preprocessing ...
% 3.23/1.26  Prover 0: Preprocessing ...
% 6.03/1.65  Prover 2: Proving ...
% 6.57/1.66  Prover 5: Proving ...
% 6.99/1.71  Prover 6: Constructing countermodel ...
% 6.99/1.71  Prover 1: Constructing countermodel ...
% 6.99/1.73  Prover 3: Constructing countermodel ...
% 7.60/1.86  Prover 2: proved (1160ms)
% 7.60/1.86  Prover 5: proved (1168ms)
% 7.60/1.86  
% 7.60/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.60/1.86  
% 7.60/1.86  
% 7.60/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.60/1.86  
% 7.60/1.88  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.60/1.88  Prover 3: stopped
% 7.60/1.88  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.60/1.88  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.31/1.90  Prover 6: stopped
% 8.31/1.91  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.31/1.93  Prover 8: Preprocessing ...
% 8.31/1.94  Prover 10: Preprocessing ...
% 8.31/1.94  Prover 7: Preprocessing ...
% 8.74/1.97  Prover 11: Preprocessing ...
% 8.74/2.02  Prover 7: Warning: ignoring some quantifiers
% 8.74/2.03  Prover 1: Found proof (size 37)
% 8.74/2.03  Prover 1: proved (1347ms)
% 8.74/2.04  Prover 7: Constructing countermodel ...
% 8.74/2.05  Prover 10: Warning: ignoring some quantifiers
% 8.74/2.05  Prover 4: Constructing countermodel ...
% 8.74/2.05  Prover 7: stopped
% 9.47/2.07  Prover 0: Proving ...
% 9.47/2.07  Prover 10: Constructing countermodel ...
% 9.47/2.07  Prover 10: stopped
% 9.47/2.08  Prover 0: stopped
% 9.47/2.08  Prover 4: stopped
% 9.47/2.08  Prover 11: stopped
% 9.72/2.11  Prover 8: Warning: ignoring some quantifiers
% 9.72/2.12  Prover 8: Constructing countermodel ...
% 9.72/2.13  Prover 8: stopped
% 9.72/2.13  
% 9.72/2.13  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.72/2.13  
% 9.93/2.14  % SZS output start Proof for theBenchmark
% 9.93/2.14  Assumptions after simplification:
% 9.93/2.14  ---------------------------------
% 9.93/2.14  
% 9.93/2.14    (ci1)
% 9.93/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.93/2.17       ~ (apart_point_and_line(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 9.93/2.17      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 9.93/2.17  
% 9.93/2.17    (ci2)
% 9.93/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.93/2.17       ~ (apart_point_and_line(v1, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 9.93/2.17      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 9.93/2.17  
% 9.93/2.17    (con)
% 9.93/2.17     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 9.93/2.17      int] :  ? [v6: int] : ( ~ (v6 = 0) &  ~ (v5 = 0) & line_connecting(v0, v1) =
% 9.93/2.17      v4 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v2) = v5 &
% 9.93/2.17      convergent_lines(v2, v3) = 0 & distinct_lines(v2, v4) = 0 &
% 9.93/2.17      distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 9.93/2.17  
% 9.93/2.17    (con1)
% 9.93/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.93/2.17       ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :  ? [v6:
% 9.93/2.17        any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 9.93/2.17        distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) |
% 9.93/2.17          v6 = 0)))
% 9.93/2.17  
% 9.93/2.17    (cu1)
% 9.93/2.18     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 9.93/2.18      (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ~ $i(v3)
% 9.93/2.18      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :  ? [v6:
% 9.93/2.18        any] :  ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 9.93/2.18        apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 9.93/2.18        apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 9.93/2.18  
% 9.93/2.18    (function-axioms)
% 9.93/2.18     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 9.93/2.18    [v3: $i] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~
% 9.93/2.18      (orthogonal_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.93/2.18      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.93/2.18      (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2)
% 9.93/2.18        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.93/2.18      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~
% 9.93/2.18      (parallel_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.93/2.18      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.93/2.18      (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0:
% 9.93/2.18      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.93/2.18    : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 9.93/2.18    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.93/2.19      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 9.93/2.19          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 9.93/2.19    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 9.93/2.19      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.93/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 9.93/2.19      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.93/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 9.93/2.19      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 9.93/2.19    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 9.93/2.19      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.93/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.93/2.19      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 9.93/2.19        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.93/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 9.93/2.19      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.93/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.93/2.19      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 9.93/2.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.93/2.19    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 9.93/2.19        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.93/2.19      $i] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0:
% 9.93/2.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.93/2.19      ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 9.93/2.19  
% 9.93/2.19  Further assumptions not needed in the proof:
% 9.93/2.19  --------------------------------------------
% 9.93/2.19  a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2,
% 9.93/2.19  ceq3, ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1,
% 9.93/2.19  ooc2, orth1, ouo1, p1, par1
% 9.93/2.19  
% 9.93/2.19  Those formulas are unsatisfiable:
% 9.93/2.19  ---------------------------------
% 9.93/2.19  
% 9.93/2.19  Begin of proof
% 9.93/2.19  | 
% 9.93/2.19  | ALPHA: (function-axioms) implies:
% 9.93/2.19  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.93/2.19  |         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 9.93/2.19  |          (distinct_points(v3, v2) = v0))
% 9.93/2.19  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.93/2.19  |         ! [v3: $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 9.93/2.19  |          (apart_point_and_line(v3, v2) = v0))
% 9.93/2.19  | 
% 9.93/2.19  | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 9.93/2.19  |        all_38_3, all_38_4, all_38_5, all_38_6 gives:
% 9.93/2.19  |   (3)   ~ (all_38_0 = 0) &  ~ (all_38_1 = 0) & line_connecting(all_38_6,
% 9.93/2.19  |          all_38_5) = all_38_2 & apart_point_and_line(all_38_5, all_38_4) =
% 9.93/2.19  |        all_38_0 & apart_point_and_line(all_38_6, all_38_4) = all_38_1 &
% 9.93/2.19  |        convergent_lines(all_38_4, all_38_3) = 0 & distinct_lines(all_38_4,
% 9.93/2.19  |          all_38_2) = 0 & distinct_points(all_38_6, all_38_5) = 0 &
% 9.93/2.19  |        $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) &
% 9.93/2.19  |        $i(all_38_6)
% 9.93/2.19  | 
% 9.93/2.19  | ALPHA: (3) implies:
% 9.93/2.19  |   (4)   ~ (all_38_1 = 0)
% 9.93/2.19  |   (5)   ~ (all_38_0 = 0)
% 9.93/2.19  |   (6)  $i(all_38_6)
% 9.93/2.19  |   (7)  $i(all_38_5)
% 9.93/2.19  |   (8)  $i(all_38_4)
% 9.93/2.19  |   (9)  $i(all_38_2)
% 9.93/2.19  |   (10)  distinct_points(all_38_6, all_38_5) = 0
% 9.93/2.19  |   (11)  distinct_lines(all_38_4, all_38_2) = 0
% 9.93/2.19  |   (12)  apart_point_and_line(all_38_6, all_38_4) = all_38_1
% 9.93/2.19  |   (13)  apart_point_and_line(all_38_5, all_38_4) = all_38_0
% 9.93/2.19  |   (14)  line_connecting(all_38_6, all_38_5) = all_38_2
% 9.93/2.19  | 
% 9.93/2.20  | GROUND_INST: instantiating (cu1) with all_38_6, all_38_5, all_38_4, all_38_2,
% 9.93/2.20  |              simplifying with (6), (7), (8), (9), (10), (11) gives:
% 9.93/2.20  |   (15)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 9.93/2.20  |         (apart_point_and_line(all_38_5, all_38_2) = v3 &
% 9.93/2.20  |           apart_point_and_line(all_38_5, all_38_4) = v2 &
% 9.93/2.20  |           apart_point_and_line(all_38_6, all_38_2) = v1 &
% 9.93/2.20  |           apart_point_and_line(all_38_6, all_38_4) = v0 & (v3 = 0 | v2 = 0 |
% 9.93/2.20  |             v1 = 0 | v0 = 0))
% 9.93/2.20  | 
% 9.93/2.20  | GROUND_INST: instantiating (con1) with all_38_6, all_38_5, all_38_2,
% 9.93/2.20  |              simplifying with (6), (7), (14) gives:
% 9.93/2.20  |   (16)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 9.93/2.20  |         (point(all_38_5) = v1 & point(all_38_6) = v0 & line(all_38_2) = v3 &
% 9.93/2.20  |           distinct_points(all_38_6, all_38_5) = v2 & ( ~ (v2 = 0) |  ~ (v1 =
% 9.93/2.20  |               0) |  ~ (v0 = 0) | v3 = 0))
% 9.93/2.20  | 
% 10.23/2.20  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2,
% 10.23/2.20  |        all_46_3 gives:
% 10.23/2.20  |   (17)  point(all_38_5) = all_46_2 & point(all_38_6) = all_46_3 &
% 10.23/2.20  |         line(all_38_2) = all_46_0 & distinct_points(all_38_6, all_38_5) =
% 10.23/2.20  |         all_46_1 & ( ~ (all_46_1 = 0) |  ~ (all_46_2 = 0) |  ~ (all_46_3 = 0)
% 10.23/2.20  |           | all_46_0 = 0)
% 10.23/2.20  | 
% 10.23/2.20  | ALPHA: (17) implies:
% 10.23/2.20  |   (18)  distinct_points(all_38_6, all_38_5) = all_46_1
% 10.23/2.20  | 
% 10.23/2.20  | DELTA: instantiating (15) with fresh symbols all_48_0, all_48_1, all_48_2,
% 10.23/2.20  |        all_48_3 gives:
% 10.23/2.20  |   (19)  apart_point_and_line(all_38_5, all_38_2) = all_48_0 &
% 10.23/2.20  |         apart_point_and_line(all_38_5, all_38_4) = all_48_1 &
% 10.23/2.20  |         apart_point_and_line(all_38_6, all_38_2) = all_48_2 &
% 10.23/2.20  |         apart_point_and_line(all_38_6, all_38_4) = all_48_3 & (all_48_0 = 0 |
% 10.23/2.20  |           all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0)
% 10.23/2.20  | 
% 10.23/2.20  | ALPHA: (19) implies:
% 10.23/2.20  |   (20)  apart_point_and_line(all_38_6, all_38_4) = all_48_3
% 10.23/2.20  |   (21)  apart_point_and_line(all_38_6, all_38_2) = all_48_2
% 10.23/2.20  |   (22)  apart_point_and_line(all_38_5, all_38_4) = all_48_1
% 10.23/2.20  |   (23)  apart_point_and_line(all_38_5, all_38_2) = all_48_0
% 10.23/2.20  |   (24)  all_48_0 = 0 | all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0
% 10.23/2.20  | 
% 10.23/2.20  | GROUND_INST: instantiating (1) with 0, all_46_1, all_38_5, all_38_6,
% 10.23/2.20  |              simplifying with (10), (18) gives:
% 10.23/2.20  |   (25)  all_46_1 = 0
% 10.23/2.20  | 
% 10.23/2.20  | GROUND_INST: instantiating (2) with all_38_1, all_48_3, all_38_4, all_38_6,
% 10.23/2.20  |              simplifying with (12), (20) gives:
% 10.23/2.20  |   (26)  all_48_3 = all_38_1
% 10.23/2.20  | 
% 10.23/2.20  | GROUND_INST: instantiating (2) with all_38_0, all_48_1, all_38_4, all_38_5,
% 10.23/2.20  |              simplifying with (13), (22) gives:
% 10.23/2.20  |   (27)  all_48_1 = all_38_0
% 10.23/2.20  | 
% 10.23/2.20  | BETA: splitting (24) gives:
% 10.23/2.20  | 
% 10.23/2.20  | Case 1:
% 10.23/2.20  | | 
% 10.23/2.20  | |   (28)  all_48_0 = 0
% 10.23/2.20  | | 
% 10.23/2.20  | | REDUCE: (23), (28) imply:
% 10.23/2.20  | |   (29)  apart_point_and_line(all_38_5, all_38_2) = 0
% 10.23/2.20  | | 
% 10.23/2.20  | | GROUND_INST: instantiating (ci2) with all_38_6, all_38_5, all_38_2,
% 10.23/2.20  | |              simplifying with (6), (7), (14), (29) gives:
% 10.23/2.20  | |   (30)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, all_38_5) =
% 10.23/2.20  | |           v0)
% 10.23/2.20  | | 
% 10.23/2.20  | | DELTA: instantiating (30) with fresh symbol all_66_0 gives:
% 10.23/2.21  | |   (31)   ~ (all_66_0 = 0) & distinct_points(all_38_6, all_38_5) = all_66_0
% 10.23/2.21  | | 
% 10.23/2.21  | | ALPHA: (31) implies:
% 10.23/2.21  | |   (32)   ~ (all_66_0 = 0)
% 10.23/2.21  | |   (33)  distinct_points(all_38_6, all_38_5) = all_66_0
% 10.23/2.21  | | 
% 10.23/2.21  | | GROUND_INST: instantiating (1) with 0, all_66_0, all_38_5, all_38_6,
% 10.23/2.21  | |              simplifying with (10), (33) gives:
% 10.23/2.21  | |   (34)  all_66_0 = 0
% 10.23/2.21  | | 
% 10.23/2.21  | | REDUCE: (32), (34) imply:
% 10.23/2.21  | |   (35)  $false
% 10.23/2.21  | | 
% 10.23/2.21  | | CLOSE: (35) is inconsistent.
% 10.23/2.21  | | 
% 10.23/2.21  | Case 2:
% 10.23/2.21  | | 
% 10.23/2.21  | |   (36)  all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0
% 10.23/2.21  | | 
% 10.23/2.21  | | BETA: splitting (36) gives:
% 10.23/2.21  | | 
% 10.23/2.21  | | Case 1:
% 10.23/2.21  | | | 
% 10.23/2.21  | | |   (37)  all_48_1 = 0
% 10.23/2.21  | | | 
% 10.23/2.21  | | | COMBINE_EQS: (27), (37) imply:
% 10.23/2.21  | | |   (38)  all_38_0 = 0
% 10.23/2.21  | | | 
% 10.23/2.21  | | | REDUCE: (5), (38) imply:
% 10.23/2.21  | | |   (39)  $false
% 10.23/2.21  | | | 
% 10.23/2.21  | | | CLOSE: (39) is inconsistent.
% 10.23/2.21  | | | 
% 10.23/2.21  | | Case 2:
% 10.23/2.21  | | | 
% 10.23/2.21  | | |   (40)  all_48_2 = 0 | all_48_3 = 0
% 10.23/2.21  | | | 
% 10.23/2.21  | | | BETA: splitting (40) gives:
% 10.23/2.21  | | | 
% 10.23/2.21  | | | Case 1:
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | |   (41)  all_48_2 = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | REDUCE: (21), (41) imply:
% 10.23/2.21  | | | |   (42)  apart_point_and_line(all_38_6, all_38_2) = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | GROUND_INST: instantiating (ci1) with all_38_6, all_38_5, all_38_2,
% 10.23/2.21  | | | |              simplifying with (6), (7), (14), (42) gives:
% 10.23/2.21  | | | |   (43)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6,
% 10.23/2.21  | | | |             all_38_5) = v0)
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | DELTA: instantiating (43) with fresh symbol all_74_0 gives:
% 10.23/2.21  | | | |   (44)   ~ (all_74_0 = 0) & distinct_points(all_38_6, all_38_5) =
% 10.23/2.21  | | | |         all_74_0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | ALPHA: (44) implies:
% 10.23/2.21  | | | |   (45)   ~ (all_74_0 = 0)
% 10.23/2.21  | | | |   (46)  distinct_points(all_38_6, all_38_5) = all_74_0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | GROUND_INST: instantiating (1) with 0, all_74_0, all_38_5, all_38_6,
% 10.23/2.21  | | | |              simplifying with (10), (46) gives:
% 10.23/2.21  | | | |   (47)  all_74_0 = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | REDUCE: (45), (47) imply:
% 10.23/2.21  | | | |   (48)  $false
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | CLOSE: (48) is inconsistent.
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | Case 2:
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | |   (49)  all_48_3 = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | COMBINE_EQS: (26), (49) imply:
% 10.23/2.21  | | | |   (50)  all_38_1 = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | SIMP: (50) implies:
% 10.23/2.21  | | | |   (51)  all_38_1 = 0
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | REDUCE: (4), (51) imply:
% 10.23/2.21  | | | |   (52)  $false
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | | CLOSE: (52) is inconsistent.
% 10.23/2.21  | | | | 
% 10.23/2.21  | | | End of split
% 10.23/2.21  | | | 
% 10.23/2.21  | | End of split
% 10.23/2.21  | | 
% 10.23/2.21  | End of split
% 10.23/2.21  | 
% 10.23/2.21  End of proof
% 10.23/2.21  % SZS output end Proof for theBenchmark
% 10.23/2.21  
% 10.23/2.21  1559ms
%------------------------------------------------------------------------------