TSTP Solution File: GEO175+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO175+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 : n004.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 23:21:51 EDT 2023

% Result   : Theorem 7.53s 1.71s
% Output   : Proof 7.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO175+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n004.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 22:55:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.07/1.01  Prover 4: Preprocessing ...
% 2.07/1.01  Prover 1: Preprocessing ...
% 2.69/1.06  Prover 6: Preprocessing ...
% 2.69/1.06  Prover 3: Preprocessing ...
% 2.69/1.06  Prover 5: Preprocessing ...
% 2.69/1.06  Prover 0: Preprocessing ...
% 2.69/1.06  Prover 2: Preprocessing ...
% 4.27/1.26  Prover 5: Proving ...
% 4.27/1.26  Prover 2: Proving ...
% 4.27/1.27  Prover 1: Constructing countermodel ...
% 4.27/1.28  Prover 3: Constructing countermodel ...
% 4.27/1.28  Prover 6: Constructing countermodel ...
% 4.89/1.36  Prover 4: Constructing countermodel ...
% 5.26/1.39  Prover 1: gave up
% 5.26/1.39  Prover 3: gave up
% 5.26/1.39  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.26/1.39  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.26/1.42  Prover 0: Proving ...
% 5.26/1.42  Prover 6: gave up
% 5.26/1.44  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.26/1.44  Prover 8: Preprocessing ...
% 5.26/1.44  Prover 7: Preprocessing ...
% 5.72/1.47  Prover 9: Preprocessing ...
% 5.72/1.48  Prover 7: Warning: ignoring some quantifiers
% 5.72/1.51  Prover 7: Constructing countermodel ...
% 5.99/1.57  Prover 8: Warning: ignoring some quantifiers
% 5.99/1.58  Prover 8: Constructing countermodel ...
% 7.05/1.64  Prover 8: gave up
% 7.05/1.64  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.05/1.68  Prover 10: Preprocessing ...
% 7.05/1.68  Prover 9: Constructing countermodel ...
% 7.05/1.69  Prover 7: Found proof (size 13)
% 7.05/1.69  Prover 7: proved (299ms)
% 7.05/1.69  Prover 9: stopped
% 7.05/1.69  Prover 2: proved (1063ms)
% 7.05/1.70  Prover 4: stopped
% 7.05/1.70  Prover 0: stopped
% 7.05/1.70  Prover 5: stopped
% 7.53/1.70  Prover 10: Warning: ignoring some quantifiers
% 7.53/1.71  Prover 10: Constructing countermodel ...
% 7.53/1.71  Prover 10: stopped
% 7.53/1.71  
% 7.53/1.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.53/1.71  
% 7.53/1.72  % SZS output start Proof for theBenchmark
% 7.53/1.72  Assumptions after simplification:
% 7.53/1.72  ---------------------------------
% 7.53/1.72  
% 7.53/1.72    (apart1)
% 7.53/1.72     ! [v0: $i] : ( ~ $i(v0) |  ~ distinct_points(v0, v0))
% 7.53/1.72  
% 7.53/1.72    (ceq3)
% 7.53/1.72     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ convergent_lines(v0,
% 7.53/1.72        v1) | distinct_lines(v0, v1))
% 7.53/1.72  
% 7.53/1.72    (con)
% 7.53/1.75     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :
% 7.53/1.75    (intersection_point(v2, v3) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 7.53/1.75      & convergent_lines(v2, v3) & distinct_points(v0, v4) & distinct_points(v0,
% 7.53/1.75        v1) &  ~ apart_point_and_line(v0, v3) &  ~ apart_point_and_line(v0, v2))
% 7.53/1.75  
% 7.53/1.75    (con2)
% 7.53/1.75     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 7.53/1.75      (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 7.53/1.75      apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) |
% 7.53/1.75      distinct_points(v2, v3)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 7.53/1.75      $i] : ( ~ (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 7.53/1.75      $i(v0) |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) |
% 7.53/1.75      distinct_points(v2, v3))
% 7.53/1.75  
% 7.53/1.75    (cu1)
% 7.53/1.75     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2)
% 7.53/1.75      |  ~ $i(v1) |  ~ $i(v0) |  ~ distinct_lines(v2, v3) |  ~ distinct_points(v0,
% 7.53/1.75        v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) |
% 7.53/1.75      apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 7.53/1.75  
% 7.53/1.75  Further assumptions not needed in the proof:
% 7.53/1.75  --------------------------------------------
% 7.53/1.75  apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, con1
% 7.53/1.75  
% 7.53/1.75  Those formulas are unsatisfiable:
% 7.53/1.75  ---------------------------------
% 7.53/1.75  
% 7.53/1.75  Begin of proof
% 7.53/1.75  | 
% 7.53/1.76  | ALPHA: (con2) implies:
% 7.53/1.76  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 7.53/1.76  |          (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 7.53/1.76  |          |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) |
% 7.53/1.76  |          distinct_points(v2, v3))
% 7.53/1.76  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 7.53/1.76  |          (intersection_point(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 7.53/1.76  |          |  ~ apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) |
% 7.53/1.76  |          distinct_points(v2, v3))
% 7.53/1.76  | 
% 7.53/1.76  | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2,
% 7.53/1.76  |        all_20_3, all_20_4 gives:
% 7.53/1.76  |   (3)  intersection_point(all_20_2, all_20_1) = all_20_0 & $i(all_20_0) &
% 7.53/1.76  |        $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) &
% 7.53/1.76  |        convergent_lines(all_20_2, all_20_1) & distinct_points(all_20_4,
% 7.53/1.76  |          all_20_0) & distinct_points(all_20_4, all_20_3) &  ~
% 7.53/1.76  |        apart_point_and_line(all_20_4, all_20_1) &  ~
% 7.53/1.76  |        apart_point_and_line(all_20_4, all_20_2)
% 7.53/1.76  | 
% 7.53/1.76  | ALPHA: (3) implies:
% 7.53/1.76  |   (4)   ~ apart_point_and_line(all_20_4, all_20_2)
% 7.53/1.76  |   (5)   ~ apart_point_and_line(all_20_4, all_20_1)
% 7.53/1.76  |   (6)  distinct_points(all_20_4, all_20_0)
% 7.53/1.76  |   (7)  convergent_lines(all_20_2, all_20_1)
% 7.53/1.76  |   (8)  $i(all_20_4)
% 7.53/1.76  |   (9)  $i(all_20_2)
% 7.53/1.76  |   (10)  $i(all_20_1)
% 7.53/1.76  |   (11)  $i(all_20_0)
% 7.53/1.76  |   (12)  intersection_point(all_20_2, all_20_1) = all_20_0
% 7.53/1.76  | 
% 7.53/1.76  | GROUND_INST: instantiating (ceq3) with all_20_2, all_20_1, simplifying with
% 7.53/1.76  |              (7), (9), (10) gives:
% 7.86/1.76  |   (13)  distinct_lines(all_20_2, all_20_1)
% 7.86/1.77  | 
% 7.86/1.77  | GROUND_INST: instantiating (cu1) with all_20_4, all_20_0, all_20_2, all_20_1,
% 7.86/1.77  |              simplifying with (4), (5), (6), (8), (9), (10), (11), (13) gives:
% 7.86/1.77  |   (14)  apart_point_and_line(all_20_0, all_20_1) |
% 7.86/1.77  |         apart_point_and_line(all_20_0, all_20_2)
% 7.86/1.77  | 
% 7.86/1.77  | BETA: splitting (14) gives:
% 7.86/1.77  | 
% 7.86/1.77  | Case 1:
% 7.86/1.77  | | 
% 7.86/1.77  | |   (15)  apart_point_and_line(all_20_0, all_20_1)
% 7.86/1.77  | | 
% 7.86/1.77  | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_20_0, all_20_0,
% 7.86/1.77  | |              simplifying with (7), (9), (10), (11), (12), (15) gives:
% 7.86/1.77  | |   (16)  distinct_points(all_20_0, all_20_0)
% 7.86/1.77  | | 
% 7.86/1.77  | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (11),
% 7.86/1.77  | |              (16) gives:
% 7.86/1.77  | |   (17)  $false
% 7.86/1.77  | | 
% 7.86/1.77  | | CLOSE: (17) is inconsistent.
% 7.86/1.77  | | 
% 7.86/1.77  | Case 2:
% 7.86/1.77  | | 
% 7.86/1.77  | |   (18)  apart_point_and_line(all_20_0, all_20_2)
% 7.86/1.77  | | 
% 7.86/1.77  | | GROUND_INST: instantiating (1) with all_20_2, all_20_1, all_20_0, all_20_0,
% 7.86/1.77  | |              simplifying with (7), (9), (10), (11), (12), (18) gives:
% 7.86/1.77  | |   (19)  distinct_points(all_20_0, all_20_0)
% 7.86/1.77  | | 
% 7.86/1.77  | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (11),
% 7.86/1.77  | |              (19) gives:
% 7.86/1.77  | |   (20)  $false
% 7.86/1.77  | | 
% 7.86/1.77  | | CLOSE: (20) is inconsistent.
% 7.86/1.77  | | 
% 7.86/1.77  | End of split
% 7.86/1.77  | 
% 7.86/1.77  End of proof
% 7.86/1.77  % SZS output end Proof for theBenchmark
% 7.86/1.77  
% 7.86/1.77  1159ms
%------------------------------------------------------------------------------