TSTP Solution File: GEO176+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO176+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 : 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 23:21:52 EDT 2023

% Result   : Theorem 7.72s 1.72s
% Output   : Proof 10.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO176+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n016.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 20:49:46 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.53/0.60  ________       _____
% 0.53/0.60  ___  __ \_________(_)________________________________
% 0.53/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.53/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.53/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.53/0.60  
% 0.53/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.53/0.60  (2023-06-19)
% 0.53/0.60  
% 0.53/0.60  (c) Philipp Rümmer, 2009-2023
% 0.53/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.53/0.60                Amanda Stjerna.
% 0.53/0.60  Free software under BSD-3-Clause.
% 0.53/0.60  
% 0.53/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.53/0.60  
% 0.53/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.53/0.61  Running up to 7 provers in parallel.
% 0.53/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.53/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.53/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.53/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.53/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.53/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.53/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.16/1.08  Prover 4: Preprocessing ...
% 3.16/1.08  Prover 1: Preprocessing ...
% 3.16/1.12  Prover 6: Preprocessing ...
% 3.16/1.12  Prover 3: Preprocessing ...
% 3.16/1.12  Prover 0: Preprocessing ...
% 3.16/1.12  Prover 2: Preprocessing ...
% 3.16/1.12  Prover 5: Preprocessing ...
% 5.94/1.45  Prover 5: Proving ...
% 5.94/1.46  Prover 2: Proving ...
% 6.65/1.54  Prover 6: Constructing countermodel ...
% 6.65/1.54  Prover 3: Constructing countermodel ...
% 6.83/1.56  Prover 1: Constructing countermodel ...
% 7.72/1.72  Prover 3: proved (1096ms)
% 7.72/1.72  
% 7.72/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.72/1.72  
% 7.72/1.72  Prover 5: stopped
% 7.72/1.72  Prover 2: stopped
% 7.72/1.72  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.72/1.73  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.72/1.73  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.72/1.73  Prover 6: stopped
% 7.72/1.75  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.48/1.78  Prover 7: Preprocessing ...
% 8.48/1.80  Prover 11: Preprocessing ...
% 8.48/1.81  Prover 10: Preprocessing ...
% 8.84/1.83  Prover 8: Preprocessing ...
% 8.84/1.84  Prover 1: Found proof (size 34)
% 8.84/1.84  Prover 1: proved (1218ms)
% 9.02/1.86  Prover 0: Proving ...
% 9.02/1.86  Prover 10: Warning: ignoring some quantifiers
% 9.02/1.87  Prover 0: stopped
% 9.02/1.88  Prover 10: Constructing countermodel ...
% 9.02/1.89  Prover 7: Warning: ignoring some quantifiers
% 9.02/1.89  Prover 4: Constructing countermodel ...
% 9.02/1.90  Prover 10: stopped
% 9.02/1.90  Prover 11: stopped
% 9.02/1.91  Prover 7: Constructing countermodel ...
% 9.02/1.91  Prover 4: stopped
% 9.02/1.91  Prover 7: stopped
% 9.57/1.97  Prover 8: Warning: ignoring some quantifiers
% 9.83/1.97  Prover 8: Constructing countermodel ...
% 9.83/1.98  Prover 8: stopped
% 9.83/1.98  
% 9.83/1.98  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.83/1.98  
% 9.83/1.99  % SZS output start Proof for theBenchmark
% 9.83/1.99  Assumptions after simplification:
% 9.83/1.99  ---------------------------------
% 9.83/1.99  
% 9.83/1.99    (ceq1)
% 9.83/2.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 9.83/2.02      (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) |  ~
% 9.83/2.02      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | apart_point_and_line(v2, v1) = 0)
% 9.83/2.02  
% 9.83/2.02    (ci3)
% 9.83/2.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.83/2.02        v2) |  ~ (apart_point_and_line(v2, v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 9.83/2.02      [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 9.83/2.02  
% 9.83/2.02    (ci4)
% 9.83/2.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.83/2.02        v2) |  ~ (apart_point_and_line(v2, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 9.83/2.02      [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 9.83/2.02  
% 9.83/2.02    (con)
% 9.83/2.03     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: any] :  ? [v5:
% 9.83/2.03      any] :  ? [v6: $i] :  ? [v7: int] : ( ~ (v7 = 0) & intersection_point(v2,
% 9.83/2.03        v3) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0,
% 9.83/2.03        v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = v7 &
% 9.83/2.03      distinct_points(v0, v1) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 9.83/2.03      (v5 = 0 | v4 = 0))
% 9.83/2.03  
% 9.83/2.03    (int1)
% 9.83/2.03     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.83/2.03        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 9.83/2.03       ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 &
% 9.83/2.03        convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) |
% 9.83/2.03          v6 = 0)))
% 9.83/2.03  
% 9.83/2.03    (function-axioms)
% 9.83/2.04     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 9.83/2.04    [v3: $i] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~
% 9.83/2.04      (orthogonal_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.83/2.04      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.83/2.04      (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2)
% 9.83/2.04        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.83/2.04      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~
% 9.83/2.04      (parallel_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.83/2.04      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.83/2.04      (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0:
% 9.83/2.04      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.83/2.04    : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 9.83/2.04    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.83/2.04      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 9.83/2.04          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 9.83/2.04    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 9.83/2.04      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.83/2.04      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 9.83/2.04      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.83/2.04      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 9.83/2.04      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 9.83/2.04    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 9.83/2.04      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.83/2.04      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.83/2.04      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 9.83/2.04        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.83/2.04      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 9.83/2.04      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.83/2.04      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.83/2.04      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 9.83/2.04      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.83/2.04    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 9.83/2.04        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.83/2.04      $i] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0:
% 9.83/2.04      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.83/2.04      ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 9.83/2.04  
% 9.83/2.04  Further assumptions not needed in the proof:
% 9.83/2.04  --------------------------------------------
% 9.83/2.05  a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq2, ceq3,
% 9.83/2.05  ci1, ci2, coipo1, con1, cotno1, couo1, cp1, cp2, cu1, cup1, oac1, occu1, ooc1,
% 9.83/2.05  ooc2, orth1, ouo1, p1, par1
% 9.83/2.05  
% 9.83/2.05  Those formulas are unsatisfiable:
% 9.83/2.05  ---------------------------------
% 9.83/2.05  
% 9.83/2.05  Begin of proof
% 9.83/2.05  | 
% 9.83/2.05  | ALPHA: (function-axioms) implies:
% 10.21/2.05  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 10.21/2.05  |         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 10.21/2.05  |          (convergent_lines(v3, v2) = v0))
% 10.21/2.05  | 
% 10.21/2.05  | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 10.21/2.05  |        all_38_3, all_38_4, all_38_5, all_38_6, all_38_7 gives:
% 10.21/2.05  |   (2)   ~ (all_38_0 = 0) & intersection_point(all_38_5, all_38_4) = all_38_1 &
% 10.21/2.05  |        apart_point_and_line(all_38_7, all_38_4) = all_38_2 &
% 10.21/2.05  |        apart_point_and_line(all_38_7, all_38_5) = all_38_3 &
% 10.21/2.05  |        convergent_lines(all_38_5, all_38_4) = 0 & distinct_points(all_38_7,
% 10.21/2.05  |          all_38_1) = all_38_0 & distinct_points(all_38_7, all_38_6) = 0 &
% 10.21/2.05  |        $i(all_38_1) & $i(all_38_4) & $i(all_38_5) & $i(all_38_6) &
% 10.21/2.05  |        $i(all_38_7) & (all_38_2 = 0 | all_38_3 = 0)
% 10.21/2.05  | 
% 10.21/2.05  | ALPHA: (2) implies:
% 10.21/2.05  |   (3)   ~ (all_38_0 = 0)
% 10.21/2.05  |   (4)  $i(all_38_7)
% 10.21/2.05  |   (5)  $i(all_38_5)
% 10.21/2.05  |   (6)  $i(all_38_4)
% 10.21/2.05  |   (7)  $i(all_38_1)
% 10.21/2.05  |   (8)  distinct_points(all_38_7, all_38_1) = all_38_0
% 10.21/2.05  |   (9)  convergent_lines(all_38_5, all_38_4) = 0
% 10.21/2.05  |   (10)  apart_point_and_line(all_38_7, all_38_5) = all_38_3
% 10.21/2.05  |   (11)  apart_point_and_line(all_38_7, all_38_4) = all_38_2
% 10.21/2.05  |   (12)  intersection_point(all_38_5, all_38_4) = all_38_1
% 10.21/2.05  |   (13)  all_38_2 = 0 | all_38_3 = 0
% 10.21/2.05  | 
% 10.21/2.05  | GROUND_INST: instantiating (int1) with all_38_5, all_38_4, all_38_1,
% 10.21/2.05  |              simplifying with (5), (6), (12) gives:
% 10.21/2.06  |   (14)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 10.21/2.06  |         (point(all_38_1) = v3 & line(all_38_4) = v1 & line(all_38_5) = v0 &
% 10.21/2.06  |           convergent_lines(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) |  ~ (v1 =
% 10.21/2.06  |               0) |  ~ (v0 = 0) | v3 = 0))
% 10.21/2.06  | 
% 10.21/2.06  | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2,
% 10.21/2.06  |        all_45_3 gives:
% 10.21/2.06  |   (15)  point(all_38_1) = all_45_0 & line(all_38_4) = all_45_2 &
% 10.21/2.06  |         line(all_38_5) = all_45_3 & convergent_lines(all_38_5, all_38_4) =
% 10.21/2.06  |         all_45_1 & ( ~ (all_45_1 = 0) |  ~ (all_45_2 = 0) |  ~ (all_45_3 = 0)
% 10.21/2.06  |           | all_45_0 = 0)
% 10.21/2.06  | 
% 10.21/2.06  | ALPHA: (15) implies:
% 10.21/2.06  |   (16)  convergent_lines(all_38_5, all_38_4) = all_45_1
% 10.21/2.06  | 
% 10.21/2.06  | GROUND_INST: instantiating (1) with 0, all_45_1, all_38_4, all_38_5,
% 10.21/2.06  |              simplifying with (9), (16) gives:
% 10.21/2.06  |   (17)  all_45_1 = 0
% 10.21/2.06  | 
% 10.21/2.06  | BETA: splitting (13) gives:
% 10.21/2.06  | 
% 10.21/2.06  | Case 1:
% 10.21/2.06  | | 
% 10.21/2.06  | |   (18)  all_38_2 = 0
% 10.21/2.06  | | 
% 10.21/2.06  | | REDUCE: (11), (18) imply:
% 10.21/2.06  | |   (19)  apart_point_and_line(all_38_7, all_38_4) = 0
% 10.21/2.06  | | 
% 10.21/2.06  | | GROUND_INST: instantiating (ceq1) with all_38_7, all_38_4, all_38_1,
% 10.21/2.06  | |              all_38_0, simplifying with (4), (6), (7), (8), (19) gives:
% 10.21/2.06  | |   (20)  all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_4) = 0
% 10.21/2.06  | | 
% 10.21/2.06  | | BETA: splitting (20) gives:
% 10.21/2.06  | | 
% 10.21/2.06  | | Case 1:
% 10.21/2.06  | | | 
% 10.21/2.06  | | |   (21)  apart_point_and_line(all_38_1, all_38_4) = 0
% 10.21/2.06  | | | 
% 10.21/2.06  | | | GROUND_INST: instantiating (ci4) with all_38_5, all_38_4, all_38_1,
% 10.21/2.06  | | |              simplifying with (5), (6), (12), (21) gives:
% 10.21/2.06  | | |   (22)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_5, all_38_4)
% 10.21/2.06  | | |           = v0)
% 10.21/2.06  | | | 
% 10.21/2.06  | | | DELTA: instantiating (22) with fresh symbol all_78_0 gives:
% 10.21/2.06  | | |   (23)   ~ (all_78_0 = 0) & convergent_lines(all_38_5, all_38_4) =
% 10.21/2.06  | | |         all_78_0
% 10.21/2.06  | | | 
% 10.21/2.06  | | | ALPHA: (23) implies:
% 10.21/2.06  | | |   (24)   ~ (all_78_0 = 0)
% 10.21/2.06  | | |   (25)  convergent_lines(all_38_5, all_38_4) = all_78_0
% 10.21/2.06  | | | 
% 10.21/2.06  | | | GROUND_INST: instantiating (1) with 0, all_78_0, all_38_4, all_38_5,
% 10.21/2.06  | | |              simplifying with (9), (25) gives:
% 10.21/2.06  | | |   (26)  all_78_0 = 0
% 10.21/2.06  | | | 
% 10.21/2.06  | | | REDUCE: (24), (26) imply:
% 10.21/2.06  | | |   (27)  $false
% 10.21/2.06  | | | 
% 10.21/2.06  | | | CLOSE: (27) is inconsistent.
% 10.21/2.06  | | | 
% 10.21/2.06  | | Case 2:
% 10.21/2.06  | | | 
% 10.21/2.06  | | |   (28)  all_38_0 = 0
% 10.21/2.06  | | | 
% 10.21/2.06  | | | REDUCE: (3), (28) imply:
% 10.21/2.06  | | |   (29)  $false
% 10.21/2.06  | | | 
% 10.21/2.06  | | | CLOSE: (29) is inconsistent.
% 10.21/2.06  | | | 
% 10.21/2.06  | | End of split
% 10.21/2.06  | | 
% 10.21/2.06  | Case 2:
% 10.21/2.06  | | 
% 10.21/2.07  | |   (30)  all_38_3 = 0
% 10.21/2.07  | | 
% 10.21/2.07  | | REDUCE: (10), (30) imply:
% 10.21/2.07  | |   (31)  apart_point_and_line(all_38_7, all_38_5) = 0
% 10.21/2.07  | | 
% 10.21/2.07  | | GROUND_INST: instantiating (ceq1) with all_38_7, all_38_5, all_38_1,
% 10.21/2.07  | |              all_38_0, simplifying with (4), (5), (7), (8), (31) gives:
% 10.21/2.07  | |   (32)  all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_5) = 0
% 10.21/2.07  | | 
% 10.21/2.07  | | BETA: splitting (32) gives:
% 10.21/2.07  | | 
% 10.21/2.07  | | Case 1:
% 10.21/2.07  | | | 
% 10.21/2.07  | | |   (33)  apart_point_and_line(all_38_1, all_38_5) = 0
% 10.21/2.07  | | | 
% 10.21/2.07  | | | GROUND_INST: instantiating (ci3) with all_38_5, all_38_4, all_38_1,
% 10.21/2.07  | | |              simplifying with (5), (6), (12), (33) gives:
% 10.21/2.07  | | |   (34)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_5, all_38_4)
% 10.21/2.07  | | |           = v0)
% 10.21/2.07  | | | 
% 10.21/2.07  | | | DELTA: instantiating (34) with fresh symbol all_78_0 gives:
% 10.21/2.07  | | |   (35)   ~ (all_78_0 = 0) & convergent_lines(all_38_5, all_38_4) =
% 10.21/2.07  | | |         all_78_0
% 10.21/2.07  | | | 
% 10.21/2.07  | | | ALPHA: (35) implies:
% 10.21/2.07  | | |   (36)   ~ (all_78_0 = 0)
% 10.21/2.07  | | |   (37)  convergent_lines(all_38_5, all_38_4) = all_78_0
% 10.21/2.07  | | | 
% 10.21/2.07  | | | GROUND_INST: instantiating (1) with 0, all_78_0, all_38_4, all_38_5,
% 10.21/2.07  | | |              simplifying with (9), (37) gives:
% 10.21/2.07  | | |   (38)  all_78_0 = 0
% 10.21/2.07  | | | 
% 10.21/2.07  | | | REDUCE: (36), (38) imply:
% 10.21/2.07  | | |   (39)  $false
% 10.21/2.07  | | | 
% 10.21/2.07  | | | CLOSE: (39) is inconsistent.
% 10.21/2.07  | | | 
% 10.21/2.07  | | Case 2:
% 10.21/2.07  | | | 
% 10.21/2.07  | | |   (40)  all_38_0 = 0
% 10.21/2.07  | | | 
% 10.21/2.07  | | | REDUCE: (3), (40) imply:
% 10.21/2.07  | | |   (41)  $false
% 10.21/2.07  | | | 
% 10.21/2.07  | | | CLOSE: (41) is inconsistent.
% 10.21/2.07  | | | 
% 10.21/2.07  | | End of split
% 10.21/2.07  | | 
% 10.21/2.07  | End of split
% 10.21/2.07  | 
% 10.21/2.07  End of proof
% 10.21/2.07  % SZS output end Proof for theBenchmark
% 10.21/2.07  
% 10.21/2.07  1471ms
%------------------------------------------------------------------------------