TSTP Solution File: GEO216+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO216+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 : n006.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 23:22:26 EDT 2023

% Result   : Theorem 7.43s 1.68s
% Output   : Proof 9.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GEO216+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33  % Computer : n006.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Aug 29 19:54:06 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.59  ________       _____
% 0.18/0.59  ___  __ \_________(_)________________________________
% 0.18/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59  
% 0.18/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59  (2023-06-19)
% 0.18/0.59  
% 0.18/0.59  (c) Philipp Rümmer, 2009-2023
% 0.18/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59                Amanda Stjerna.
% 0.18/0.59  Free software under BSD-3-Clause.
% 0.18/0.59  
% 0.18/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59  
% 0.18/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60  Running up to 7 provers in parallel.
% 0.61/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.61/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.61/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.61/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.61/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.61/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.61/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.11  Prover 4: Preprocessing ...
% 3.32/1.11  Prover 1: Preprocessing ...
% 3.32/1.16  Prover 5: Preprocessing ...
% 3.32/1.16  Prover 3: Preprocessing ...
% 3.32/1.16  Prover 2: Preprocessing ...
% 3.32/1.16  Prover 6: Preprocessing ...
% 3.32/1.17  Prover 0: Preprocessing ...
% 5.80/1.51  Prover 2: Proving ...
% 5.80/1.52  Prover 5: Proving ...
% 6.36/1.56  Prover 6: Constructing countermodel ...
% 6.72/1.58  Prover 1: Constructing countermodel ...
% 6.72/1.58  Prover 3: Constructing countermodel ...
% 7.43/1.67  Prover 3: proved (1062ms)
% 7.43/1.68  
% 7.43/1.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/1.68  
% 7.43/1.68  Prover 6: proved (1061ms)
% 7.43/1.68  
% 7.43/1.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.43/1.68  
% 7.43/1.68  Prover 2: stopped
% 7.43/1.68  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.43/1.69  Prover 5: stopped
% 7.43/1.69  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.43/1.69  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.43/1.69  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.84/1.76  Prover 8: Preprocessing ...
% 7.84/1.77  Prover 7: Preprocessing ...
% 7.84/1.77  Prover 11: Preprocessing ...
% 7.84/1.77  Prover 10: Preprocessing ...
% 8.30/1.83  Prover 1: Found proof (size 20)
% 8.30/1.83  Prover 1: proved (1221ms)
% 8.30/1.85  Prover 10: Warning: ignoring some quantifiers
% 8.30/1.87  Prover 7: Warning: ignoring some quantifiers
% 8.30/1.87  Prover 11: stopped
% 8.99/1.89  Prover 10: Constructing countermodel ...
% 8.99/1.90  Prover 10: stopped
% 8.99/1.90  Prover 7: Constructing countermodel ...
% 8.99/1.91  Prover 7: stopped
% 9.31/1.94  Prover 8: Warning: ignoring some quantifiers
% 9.40/1.94  Prover 4: Constructing countermodel ...
% 9.40/1.95  Prover 8: Constructing countermodel ...
% 9.40/1.96  Prover 8: stopped
% 9.40/1.96  Prover 0: Proving ...
% 9.40/1.97  Prover 4: stopped
% 9.40/1.97  Prover 0: stopped
% 9.40/1.97  
% 9.40/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.40/1.97  
% 9.40/1.98  % SZS output start Proof for theBenchmark
% 9.40/1.98  Assumptions after simplification:
% 9.40/1.98  ---------------------------------
% 9.40/1.98  
% 9.40/1.98    (a5)
% 9.79/2.01     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (orthogonal_lines(v0,
% 9.79/2.01          v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) &  !
% 9.79/2.01    [v0: $i] :  ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ~ $i(v1) |  ~
% 9.79/2.01      $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 9.79/2.01  
% 9.79/2.01    (coipo1)
% 9.79/2.01     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 9.79/2.01      (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 9.79/2.01      convergent_lines(v0, v1) = 0)
% 9.79/2.01  
% 9.79/2.01    (con)
% 9.79/2.01     ? [v0: $i] : (orthogonal_lines(v0, v0) = 0 & $i(v0))
% 9.79/2.01  
% 9.79/2.01    (couo1)
% 9.79/2.01     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] :  ! [v4: int] : (v4 =
% 9.79/2.01      0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~
% 9.79/2.01      (unorthogonal_lines(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 9.79/2.01      [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 9.79/2.01  
% 9.79/2.01    (occu1)
% 9.79/2.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 9.79/2.02      (unorthogonal_lines(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 9.79/2.02      convergent_lines(v0, v1) = 0)
% 9.79/2.02  
% 9.79/2.02    (function-axioms)
% 9.79/2.03     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 9.79/2.03    [v3: $i] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~
% 9.79/2.03      (orthogonal_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.79/2.03      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.79/2.03      (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2)
% 9.79/2.03        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.79/2.03      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~
% 9.79/2.03      (parallel_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.79/2.03      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.79/2.03      (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0:
% 9.79/2.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.79/2.03    : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 9.79/2.03    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.79/2.03      (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3,
% 9.79/2.03          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 9.79/2.03    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) | 
% 9.79/2.03      ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.79/2.03      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~
% 9.79/2.03      (parallel_through_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 9.79/2.03      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~
% 9.79/2.03      (intersection_point(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 9.79/2.03    :  ! [v3: $i] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~
% 9.79/2.03      (line_connecting(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.79/2.03      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.79/2.03      (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) =
% 9.79/2.03        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.79/2.03      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 9.79/2.03      (convergent_lines(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 9.79/2.03      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 9.79/2.03      (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0:
% 9.79/2.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 9.79/2.03    : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) =
% 9.79/2.03        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 9.79/2.03      $i] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0:
% 9.79/2.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 9.79/2.03      ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 9.79/2.03  
% 9.79/2.03  Further assumptions not needed in the proof:
% 9.79/2.03  --------------------------------------------
% 9.79/2.03  a3, a4, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3,
% 9.79/2.03  ci1, ci2, ci3, ci4, con1, cotno1, cp1, cp2, cu1, cup1, int1, oac1, ooc1, ooc2,
% 9.79/2.03  orth1, ouo1, p1, par1
% 9.79/2.03  
% 9.79/2.03  Those formulas are unsatisfiable:
% 9.79/2.03  ---------------------------------
% 9.79/2.03  
% 9.79/2.03  Begin of proof
% 9.79/2.03  | 
% 9.79/2.03  | ALPHA: (a5) implies:
% 9.79/2.03  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ~
% 9.79/2.03  |          $i(v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) &
% 9.79/2.03  |            unorthogonal_lines(v0, v1) = v2))
% 9.79/2.03  | 
% 9.79/2.03  | ALPHA: (function-axioms) implies:
% 9.79/2.03  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 9.79/2.03  |         ! [v3: $i] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~
% 9.79/2.03  |          (convergent_lines(v3, v2) = v0))
% 9.79/2.03  | 
% 9.79/2.03  | DELTA: instantiating (con) with fresh symbol all_38_0 gives:
% 9.79/2.03  |   (3)  orthogonal_lines(all_38_0, all_38_0) = 0 & $i(all_38_0)
% 9.79/2.03  | 
% 9.79/2.03  | ALPHA: (3) implies:
% 9.79/2.03  |   (4)  $i(all_38_0)
% 9.79/2.03  |   (5)  orthogonal_lines(all_38_0, all_38_0) = 0
% 9.79/2.03  | 
% 9.79/2.04  | GROUND_INST: instantiating (1) with all_38_0, all_38_0, simplifying with (4),
% 9.79/2.04  |              (5) gives:
% 9.79/2.04  |   (6)   ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_0, all_38_0) =
% 9.79/2.04  |          v0)
% 9.79/2.04  | 
% 9.79/2.04  | DELTA: instantiating (6) with fresh symbol all_45_0 gives:
% 9.79/2.04  |   (7)   ~ (all_45_0 = 0) & unorthogonal_lines(all_38_0, all_38_0) = all_45_0
% 9.79/2.04  | 
% 9.79/2.04  | ALPHA: (7) implies:
% 9.79/2.04  |   (8)   ~ (all_45_0 = 0)
% 9.79/2.04  |   (9)  unorthogonal_lines(all_38_0, all_38_0) = all_45_0
% 9.79/2.04  | 
% 9.79/2.04  | GROUND_INST: instantiating (couo1) with all_38_0, all_38_0, all_38_0,
% 9.79/2.04  |              all_45_0, all_45_0, simplifying with (4), (9) gives:
% 9.79/2.04  |   (10)  all_45_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) &
% 9.79/2.04  |           convergent_lines(all_38_0, all_38_0) = v0)
% 9.79/2.04  | 
% 9.79/2.04  | GROUND_INST: instantiating (occu1) with all_38_0, all_38_0, all_45_0,
% 9.79/2.04  |              simplifying with (4), (9) gives:
% 9.79/2.04  |   (11)  all_45_0 = 0 | convergent_lines(all_38_0, all_38_0) = 0
% 9.79/2.04  | 
% 9.79/2.04  | BETA: splitting (11) gives:
% 9.79/2.04  | 
% 9.79/2.04  | Case 1:
% 9.79/2.04  | | 
% 9.79/2.04  | |   (12)  convergent_lines(all_38_0, all_38_0) = 0
% 9.79/2.04  | | 
% 9.79/2.04  | | BETA: splitting (10) gives:
% 9.79/2.04  | | 
% 9.79/2.04  | | Case 1:
% 9.79/2.04  | | | 
% 9.79/2.04  | | |   (13)  all_45_0 = 0
% 9.79/2.04  | | | 
% 9.79/2.04  | | | REDUCE: (8), (13) imply:
% 9.79/2.04  | | |   (14)  $false
% 9.79/2.04  | | | 
% 9.79/2.04  | | | CLOSE: (14) is inconsistent.
% 9.79/2.04  | | | 
% 9.79/2.04  | | Case 2:
% 9.79/2.04  | | | 
% 9.79/2.04  | | |   (15)   ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_0, all_38_0)
% 9.79/2.04  | | |           = v0)
% 9.79/2.04  | | | 
% 9.79/2.04  | | | DELTA: instantiating (15) with fresh symbol all_62_0 gives:
% 9.79/2.04  | | |   (16)   ~ (all_62_0 = 0) & convergent_lines(all_38_0, all_38_0) =
% 9.79/2.04  | | |         all_62_0
% 9.79/2.04  | | | 
% 9.79/2.04  | | | ALPHA: (16) implies:
% 9.79/2.04  | | |   (17)   ~ (all_62_0 = 0)
% 9.79/2.04  | | |   (18)  convergent_lines(all_38_0, all_38_0) = all_62_0
% 9.79/2.04  | | | 
% 9.79/2.04  | | | GROUND_INST: instantiating (2) with 0, all_62_0, all_38_0, all_38_0,
% 9.79/2.04  | | |              simplifying with (12), (18) gives:
% 9.79/2.04  | | |   (19)  all_62_0 = 0
% 9.79/2.04  | | | 
% 9.79/2.04  | | | REDUCE: (17), (19) imply:
% 9.79/2.04  | | |   (20)  $false
% 9.79/2.04  | | | 
% 9.79/2.04  | | | CLOSE: (20) is inconsistent.
% 9.79/2.04  | | | 
% 9.79/2.04  | | End of split
% 9.79/2.04  | | 
% 9.79/2.04  | Case 2:
% 9.79/2.04  | | 
% 9.79/2.04  | |   (21)  all_45_0 = 0
% 9.79/2.04  | | 
% 9.79/2.04  | | REDUCE: (8), (21) imply:
% 9.79/2.04  | |   (22)  $false
% 9.79/2.04  | | 
% 9.79/2.04  | | CLOSE: (22) is inconsistent.
% 9.79/2.04  | | 
% 9.79/2.04  | End of split
% 9.79/2.04  | 
% 9.79/2.04  End of proof
% 9.79/2.04  % SZS output end Proof for theBenchmark
% 9.79/2.04  
% 9.79/2.04  1453ms
%------------------------------------------------------------------------------