TSTP Solution File: GEO179+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO179+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 23:21:55 EDT 2023

% Result   : Theorem 8.49s 1.87s
% Output   : Proof 10.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO179+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % 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 20:12:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.59  ________       _____
% 0.20/0.59  ___  __ \_________(_)________________________________
% 0.20/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59  (2023-06-19)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2023
% 0.20/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59                Amanda Stjerna.
% 0.20/0.59  Free software under BSD-3-Clause.
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60  Running up to 7 provers in parallel.
% 0.66/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.86/1.14  Prover 4: Preprocessing ...
% 2.86/1.14  Prover 1: Preprocessing ...
% 3.56/1.18  Prover 6: Preprocessing ...
% 3.56/1.18  Prover 5: Preprocessing ...
% 3.56/1.18  Prover 2: Preprocessing ...
% 3.56/1.18  Prover 0: Preprocessing ...
% 3.56/1.19  Prover 3: Preprocessing ...
% 6.28/1.57  Prover 2: Proving ...
% 6.28/1.57  Prover 5: Proving ...
% 6.96/1.65  Prover 6: Constructing countermodel ...
% 6.96/1.67  Prover 3: Constructing countermodel ...
% 6.96/1.67  Prover 1: Constructing countermodel ...
% 8.49/1.87  Prover 6: proved (1250ms)
% 8.49/1.87  
% 8.49/1.87  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.49/1.87  
% 8.49/1.89  Prover 3: proved (1251ms)
% 8.49/1.89  
% 8.49/1.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.49/1.89  
% 8.49/1.90  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.49/1.90  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.49/1.90  Prover 2: stopped
% 8.49/1.91  Prover 5: stopped
% 9.07/1.93  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.07/1.93  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.07/1.95  Prover 7: Preprocessing ...
% 9.07/1.95  Prover 4: Constructing countermodel ...
% 9.07/1.96  Prover 10: Preprocessing ...
% 9.07/1.97  Prover 8: Preprocessing ...
% 9.07/1.97  Prover 11: Preprocessing ...
% 9.07/1.98  Prover 0: Proving ...
% 9.49/2.00  Prover 0: stopped
% 9.49/2.02  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.49/2.02  Prover 7: Warning: ignoring some quantifiers
% 9.49/2.04  Prover 7: Constructing countermodel ...
% 9.49/2.04  Prover 10: Warning: ignoring some quantifiers
% 10.09/2.06  Prover 1: Found proof (size 52)
% 10.09/2.06  Prover 1: proved (1446ms)
% 10.09/2.06  Prover 13: Preprocessing ...
% 10.09/2.06  Prover 11: stopped
% 10.09/2.07  Prover 10: Constructing countermodel ...
% 10.09/2.07  Prover 7: stopped
% 10.09/2.07  Prover 4: stopped
% 10.22/2.07  Prover 10: stopped
% 10.22/2.09  Prover 13: stopped
% 10.22/2.11  Prover 8: Warning: ignoring some quantifiers
% 10.46/2.12  Prover 8: Constructing countermodel ...
% 10.46/2.13  Prover 8: stopped
% 10.46/2.13  
% 10.46/2.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.46/2.13  
% 10.46/2.14  % SZS output start Proof for theBenchmark
% 10.58/2.14  Assumptions after simplification:
% 10.58/2.14  ---------------------------------
% 10.58/2.14  
% 10.58/2.14    (ceq1)
% 10.58/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 10.58/2.17      (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) |  ~
% 10.58/2.17      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | apart_point_and_line(v2, v1) = 0)
% 10.58/2.17  
% 10.58/2.17    (ceq2)
% 10.58/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 10.58/2.17      (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) |  ~
% 10.58/2.17      $i(v2) |  ~ $i(v1) |  ~ $i(v0) | apart_point_and_line(v0, v2) = 0)
% 10.58/2.17  
% 10.58/2.17    (ci1)
% 10.58/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.58/2.17       ~ (apart_point_and_line(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 10.58/2.17      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.58/2.17  
% 10.58/2.17    (ci2)
% 10.58/2.17     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 10.58/2.17       ~ (apart_point_and_line(v1, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int]
% 10.58/2.17      : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 10.58/2.17  
% 10.58/2.17    (con)
% 10.58/2.18     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5:
% 10.58/2.18      any] :  ? [v6: $i] :  ? [v7: any] : (line_connecting(v2, v1) = v6 &
% 10.58/2.18      line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 &
% 10.58/2.18      apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 &
% 10.58/2.18      distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 0 & $i(v6) & $i(v4)
% 10.58/2.18      & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) |  ~ (v5 = 0)))
% 10.58/2.18  
% 10.58/2.18    (cu1)
% 10.58/2.18     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 10.58/2.18      (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ~ $i(v3)
% 10.58/2.18      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :  ? [v6:
% 10.58/2.18        any] :  ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 10.58/2.18        apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 10.58/2.18        apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 10.58/2.18  
% 10.58/2.18    (function-axioms)
% 10.58/2.19     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 10.58/2.19    [v3: $i] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~
% 10.58/2.19      (orthogonal_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.58/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.58/2.19      (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2)
% 10.58/2.19        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.58/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~
% 10.58/2.19      (parallel_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.58/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.58/2.19      (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0:
% 10.58/2.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 10.58/2.19    : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 10.58/2.19    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.58/2.19      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 10.58/2.19          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 10.58/2.19    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 10.58/2.19      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 10.58/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 10.58/2.19      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 10.58/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 10.58/2.19      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 10.58/2.19    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 10.58/2.19      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.58/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.58/2.19      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 10.58/2.19        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.58/2.19      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 10.58/2.19      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 10.58/2.19      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.58/2.19      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 10.58/2.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 10.58/2.19    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 10.58/2.19        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.58/2.19      $i] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0:
% 10.58/2.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 10.58/2.19      ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 10.58/2.19  
% 10.58/2.19  Further assumptions not needed in the proof:
% 10.58/2.19  --------------------------------------------
% 10.58/2.19  a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq3, ci3,
% 10.58/2.19  ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2,
% 10.58/2.19  orth1, ouo1, p1, par1
% 10.58/2.19  
% 10.58/2.19  Those formulas are unsatisfiable:
% 10.58/2.19  ---------------------------------
% 10.58/2.19  
% 10.58/2.19  Begin of proof
% 10.58/2.19  | 
% 10.58/2.19  | ALPHA: (function-axioms) implies:
% 10.58/2.20  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 10.58/2.20  |         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 10.58/2.20  |          (distinct_points(v3, v2) = v0))
% 10.58/2.20  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 10.58/2.20  |         ! [v3: $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 10.58/2.20  |          (apart_point_and_line(v3, v2) = v0))
% 10.58/2.20  | 
% 10.58/2.20  | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 10.58/2.20  |        all_38_3, all_38_4, all_38_5, all_38_6, all_38_7 gives:
% 10.58/2.20  |   (3)  line_connecting(all_38_5, all_38_6) = all_38_1 &
% 10.58/2.20  |        line_connecting(all_38_5, all_38_7) = all_38_3 &
% 10.58/2.20  |        line_connecting(all_38_7, all_38_6) = all_38_4 &
% 10.58/2.20  |        apart_point_and_line(all_38_5, all_38_4) = 0 & distinct_lines(all_38_4,
% 10.58/2.20  |          all_38_1) = all_38_0 & distinct_lines(all_38_4, all_38_3) = all_38_2
% 10.58/2.20  |        & distinct_points(all_38_7, all_38_6) = 0 & $i(all_38_1) & $i(all_38_3)
% 10.58/2.20  |        & $i(all_38_4) & $i(all_38_5) & $i(all_38_6) & $i(all_38_7) & ( ~
% 10.58/2.20  |          (all_38_0 = 0) |  ~ (all_38_2 = 0))
% 10.58/2.20  | 
% 10.58/2.20  | ALPHA: (3) implies:
% 10.58/2.20  |   (4)  $i(all_38_7)
% 10.58/2.20  |   (5)  $i(all_38_6)
% 10.58/2.20  |   (6)  $i(all_38_5)
% 10.58/2.20  |   (7)  $i(all_38_4)
% 10.58/2.20  |   (8)  $i(all_38_3)
% 10.58/2.20  |   (9)  $i(all_38_1)
% 10.58/2.20  |   (10)  distinct_points(all_38_7, all_38_6) = 0
% 10.58/2.20  |   (11)  distinct_lines(all_38_4, all_38_3) = all_38_2
% 10.58/2.20  |   (12)  distinct_lines(all_38_4, all_38_1) = all_38_0
% 10.58/2.20  |   (13)  apart_point_and_line(all_38_5, all_38_4) = 0
% 10.58/2.20  |   (14)  line_connecting(all_38_7, all_38_6) = all_38_4
% 10.58/2.20  |   (15)  line_connecting(all_38_5, all_38_7) = all_38_3
% 10.58/2.20  |   (16)  line_connecting(all_38_5, all_38_6) = all_38_1
% 10.58/2.20  |   (17)   ~ (all_38_0 = 0) |  ~ (all_38_2 = 0)
% 10.58/2.20  | 
% 10.58/2.20  | GROUND_INST: instantiating (ceq2) with all_38_5, all_38_4, all_38_1, all_38_0,
% 10.58/2.20  |              simplifying with (6), (7), (9), (12), (13) gives:
% 10.58/2.20  |   (18)  all_38_0 = 0 | apart_point_and_line(all_38_5, all_38_1) = 0
% 10.58/2.20  | 
% 10.58/2.20  | GROUND_INST: instantiating (ceq2) with all_38_5, all_38_4, all_38_3, all_38_2,
% 10.58/2.20  |              simplifying with (6), (7), (8), (11), (13) gives:
% 10.58/2.20  |   (19)  all_38_2 = 0 | apart_point_and_line(all_38_5, all_38_3) = 0
% 10.58/2.20  | 
% 10.58/2.20  | BETA: splitting (17) gives:
% 10.58/2.20  | 
% 10.58/2.20  | Case 1:
% 10.58/2.20  | | 
% 10.58/2.20  | |   (20)   ~ (all_38_0 = 0)
% 10.58/2.20  | | 
% 10.58/2.20  | | BETA: splitting (18) gives:
% 10.58/2.20  | | 
% 10.58/2.20  | | Case 1:
% 10.58/2.20  | | | 
% 10.58/2.20  | | |   (21)  apart_point_and_line(all_38_5, all_38_1) = 0
% 10.58/2.20  | | | 
% 10.58/2.21  | | | GROUND_INST: instantiating (ci1) with all_38_5, all_38_6, all_38_1,
% 10.58/2.21  | | |              simplifying with (5), (6), (16), (21) gives:
% 10.58/2.21  | | |   (22)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_6)
% 10.58/2.21  | | |           = v0)
% 10.58/2.21  | | | 
% 10.58/2.21  | | | DELTA: instantiating (22) with fresh symbol all_56_0 gives:
% 10.58/2.21  | | |   (23)   ~ (all_56_0 = 0) & distinct_points(all_38_5, all_38_6) = all_56_0
% 10.58/2.21  | | | 
% 10.58/2.21  | | | ALPHA: (23) implies:
% 10.58/2.21  | | |   (24)   ~ (all_56_0 = 0)
% 10.58/2.21  | | |   (25)  distinct_points(all_38_5, all_38_6) = all_56_0
% 10.58/2.21  | | | 
% 10.58/2.21  | | | GROUND_INST: instantiating (ceq1) with all_38_5, all_38_1, all_38_6,
% 10.58/2.21  | | |              all_56_0, simplifying with (5), (6), (9), (21), (25) gives:
% 10.58/2.21  | | |   (26)  all_56_0 = 0 | apart_point_and_line(all_38_6, all_38_1) = 0
% 10.58/2.21  | | | 
% 10.58/2.21  | | | GROUND_INST: instantiating (ceq1) with all_38_5, all_38_4, all_38_6,
% 10.58/2.21  | | |              all_56_0, simplifying with (5), (6), (7), (13), (25) gives:
% 10.58/2.21  | | |   (27)  all_56_0 = 0 | apart_point_and_line(all_38_6, all_38_4) = 0
% 10.58/2.21  | | | 
% 10.58/2.21  | | | BETA: splitting (27) gives:
% 10.58/2.21  | | | 
% 10.58/2.21  | | | Case 1:
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | |   (28)  apart_point_and_line(all_38_6, all_38_4) = 0
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | | BETA: splitting (26) gives:
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | | Case 1:
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | GROUND_INST: instantiating (ci2) with all_38_7, all_38_6, all_38_4,
% 10.58/2.21  | | | | |              simplifying with (4), (5), (14), (28) gives:
% 10.58/2.21  | | | | |   (29)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_7,
% 10.58/2.21  | | | | |             all_38_6) = v0)
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | DELTA: instantiating (29) with fresh symbol all_80_0 gives:
% 10.58/2.21  | | | | |   (30)   ~ (all_80_0 = 0) & distinct_points(all_38_7, all_38_6) =
% 10.58/2.21  | | | | |         all_80_0
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | ALPHA: (30) implies:
% 10.58/2.21  | | | | |   (31)   ~ (all_80_0 = 0)
% 10.58/2.21  | | | | |   (32)  distinct_points(all_38_7, all_38_6) = all_80_0
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | GROUND_INST: instantiating (1) with 0, all_80_0, all_38_6, all_38_7,
% 10.58/2.21  | | | | |              simplifying with (10), (32) gives:
% 10.58/2.21  | | | | |   (33)  all_80_0 = 0
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | REDUCE: (31), (33) imply:
% 10.58/2.21  | | | | |   (34)  $false
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | CLOSE: (34) is inconsistent.
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | Case 2:
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | |   (35)  all_56_0 = 0
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | REDUCE: (24), (35) imply:
% 10.58/2.21  | | | | |   (36)  $false
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | | CLOSE: (36) is inconsistent.
% 10.58/2.21  | | | | | 
% 10.58/2.21  | | | | End of split
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | Case 2:
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | |   (37)  all_56_0 = 0
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | | REDUCE: (24), (37) imply:
% 10.58/2.21  | | | |   (38)  $false
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | | CLOSE: (38) is inconsistent.
% 10.58/2.21  | | | | 
% 10.58/2.21  | | | End of split
% 10.58/2.21  | | | 
% 10.58/2.21  | | Case 2:
% 10.58/2.21  | | | 
% 10.58/2.21  | | |   (39)  all_38_0 = 0
% 10.58/2.21  | | | 
% 10.58/2.21  | | | REDUCE: (20), (39) imply:
% 10.58/2.21  | | |   (40)  $false
% 10.58/2.21  | | | 
% 10.58/2.21  | | | CLOSE: (40) is inconsistent.
% 10.58/2.21  | | | 
% 10.58/2.21  | | End of split
% 10.58/2.21  | | 
% 10.58/2.21  | Case 2:
% 10.58/2.21  | | 
% 10.58/2.21  | |   (41)  all_38_0 = 0
% 10.58/2.21  | |   (42)   ~ (all_38_2 = 0)
% 10.58/2.21  | | 
% 10.58/2.21  | | REDUCE: (12), (41) imply:
% 10.58/2.21  | |   (43)  distinct_lines(all_38_4, all_38_1) = 0
% 10.58/2.21  | | 
% 10.58/2.21  | | BETA: splitting (19) gives:
% 10.58/2.21  | | 
% 10.58/2.21  | | Case 1:
% 10.58/2.21  | | | 
% 10.58/2.22  | | |   (44)  apart_point_and_line(all_38_5, all_38_3) = 0
% 10.58/2.22  | | | 
% 10.58/2.22  | | | GROUND_INST: instantiating (cu1) with all_38_7, all_38_6, all_38_4,
% 10.58/2.22  | | |              all_38_1, simplifying with (4), (5), (7), (9), (10), (43)
% 10.58/2.22  | | |              gives:
% 10.58/2.22  | | |   (45)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 10.58/2.22  | | |         (apart_point_and_line(all_38_6, all_38_1) = v3 &
% 10.58/2.22  | | |           apart_point_and_line(all_38_6, all_38_4) = v2 &
% 10.58/2.22  | | |           apart_point_and_line(all_38_7, all_38_1) = v1 &
% 10.58/2.22  | | |           apart_point_and_line(all_38_7, all_38_4) = v0 & (v3 = 0 | v2 = 0
% 10.58/2.22  | | |             | v1 = 0 | v0 = 0))
% 10.58/2.22  | | | 
% 10.58/2.22  | | | GROUND_INST: instantiating (ci1) with all_38_5, all_38_7, all_38_3,
% 10.58/2.22  | | |              simplifying with (4), (6), (15), (44) gives:
% 10.58/2.22  | | |   (46)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_7)
% 10.58/2.22  | | |           = v0)
% 10.58/2.22  | | | 
% 10.58/2.22  | | | DELTA: instantiating (46) with fresh symbol all_57_0 gives:
% 10.58/2.22  | | |   (47)   ~ (all_57_0 = 0) & distinct_points(all_38_5, all_38_7) = all_57_0
% 10.58/2.22  | | | 
% 10.58/2.22  | | | ALPHA: (47) implies:
% 10.58/2.22  | | |   (48)   ~ (all_57_0 = 0)
% 10.58/2.22  | | |   (49)  distinct_points(all_38_5, all_38_7) = all_57_0
% 10.58/2.22  | | | 
% 10.58/2.22  | | | DELTA: instantiating (45) with fresh symbols all_59_0, all_59_1, all_59_2,
% 10.58/2.22  | | |        all_59_3 gives:
% 10.58/2.22  | | |   (50)  apart_point_and_line(all_38_6, all_38_1) = all_59_0 &
% 10.58/2.22  | | |         apart_point_and_line(all_38_6, all_38_4) = all_59_1 &
% 10.58/2.22  | | |         apart_point_and_line(all_38_7, all_38_1) = all_59_2 &
% 10.58/2.22  | | |         apart_point_and_line(all_38_7, all_38_4) = all_59_3 & (all_59_0 =
% 10.58/2.22  | | |           0 | all_59_1 = 0 | all_59_2 = 0 | all_59_3 = 0)
% 10.58/2.22  | | | 
% 10.58/2.22  | | | ALPHA: (50) implies:
% 10.58/2.22  | | |   (51)  apart_point_and_line(all_38_7, all_38_4) = all_59_3
% 10.58/2.22  | | | 
% 10.58/2.22  | | | GROUND_INST: instantiating (ceq1) with all_38_5, all_38_4, all_38_7,
% 10.58/2.22  | | |              all_57_0, simplifying with (4), (6), (7), (13), (49) gives:
% 10.58/2.22  | | |   (52)  all_57_0 = 0 | apart_point_and_line(all_38_7, all_38_4) = 0
% 10.58/2.22  | | | 
% 10.58/2.22  | | | BETA: splitting (52) gives:
% 10.58/2.22  | | | 
% 10.58/2.22  | | | Case 1:
% 10.58/2.22  | | | | 
% 10.58/2.22  | | | |   (53)  apart_point_and_line(all_38_7, all_38_4) = 0
% 10.58/2.22  | | | | 
% 10.58/2.22  | | | | GROUND_INST: instantiating (2) with all_59_3, 0, all_38_4, all_38_7,
% 10.58/2.22  | | | |              simplifying with (51), (53) gives:
% 10.58/2.22  | | | |   (54)  all_59_3 = 0
% 10.58/2.22  | | | | 
% 10.99/2.22  | | | | GROUND_INST: instantiating (ci1) with all_38_7, all_38_6, all_38_4,
% 10.99/2.22  | | | |              simplifying with (4), (5), (14), (53) gives:
% 10.99/2.22  | | | |   (55)   ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_7,
% 10.99/2.22  | | | |             all_38_6) = v0)
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | DELTA: instantiating (55) with fresh symbol all_90_0 gives:
% 10.99/2.22  | | | |   (56)   ~ (all_90_0 = 0) & distinct_points(all_38_7, all_38_6) =
% 10.99/2.22  | | | |         all_90_0
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | ALPHA: (56) implies:
% 10.99/2.22  | | | |   (57)   ~ (all_90_0 = 0)
% 10.99/2.22  | | | |   (58)  distinct_points(all_38_7, all_38_6) = all_90_0
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | GROUND_INST: instantiating (1) with 0, all_90_0, all_38_6, all_38_7,
% 10.99/2.22  | | | |              simplifying with (10), (58) gives:
% 10.99/2.22  | | | |   (59)  all_90_0 = 0
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | REDUCE: (57), (59) imply:
% 10.99/2.22  | | | |   (60)  $false
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | CLOSE: (60) is inconsistent.
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | Case 2:
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | |   (61)  all_57_0 = 0
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | REDUCE: (48), (61) imply:
% 10.99/2.22  | | | |   (62)  $false
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | | CLOSE: (62) is inconsistent.
% 10.99/2.22  | | | | 
% 10.99/2.22  | | | End of split
% 10.99/2.22  | | | 
% 10.99/2.22  | | Case 2:
% 10.99/2.22  | | | 
% 10.99/2.22  | | |   (63)  all_38_2 = 0
% 10.99/2.22  | | | 
% 10.99/2.23  | | | REDUCE: (42), (63) imply:
% 10.99/2.23  | | |   (64)  $false
% 10.99/2.23  | | | 
% 10.99/2.23  | | | CLOSE: (64) is inconsistent.
% 10.99/2.23  | | | 
% 10.99/2.23  | | End of split
% 10.99/2.23  | | 
% 10.99/2.23  | End of split
% 10.99/2.23  | 
% 10.99/2.23  End of proof
% 10.99/2.23  % SZS output end Proof for theBenchmark
% 10.99/2.23  
% 10.99/2.23  1632ms
%------------------------------------------------------------------------------