TSTP Solution File: GEO178+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEO178+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 : n026.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 23:21:54 EDT 2023

% Result   : Theorem 5.09s 1.48s
% Output   : Proof 6.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO178+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35  % Computer : n026.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Tue Aug 29 22:51:35 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  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 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 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 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 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
% 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
% 2.30/1.05  Prover 1: Preprocessing ...
% 2.30/1.06  Prover 4: Preprocessing ...
% 2.30/1.10  Prover 5: Preprocessing ...
% 2.30/1.10  Prover 0: Preprocessing ...
% 2.30/1.10  Prover 2: Preprocessing ...
% 2.30/1.10  Prover 6: Preprocessing ...
% 2.30/1.10  Prover 3: Preprocessing ...
% 4.47/1.33  Prover 5: Proving ...
% 4.47/1.34  Prover 2: Proving ...
% 4.47/1.35  Prover 6: Constructing countermodel ...
% 4.47/1.35  Prover 3: Constructing countermodel ...
% 4.47/1.36  Prover 1: Constructing countermodel ...
% 5.09/1.46  Prover 4: Constructing countermodel ...
% 5.09/1.48  Prover 3: proved (837ms)
% 5.09/1.48  
% 5.09/1.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/1.48  
% 5.09/1.48  Prover 6: proved (835ms)
% 5.09/1.48  
% 5.09/1.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.09/1.48  
% 5.73/1.49  Prover 2: stopped
% 5.73/1.50  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.73/1.50  Prover 5: proved (844ms)
% 5.73/1.50  
% 5.73/1.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/1.50  
% 5.73/1.50  Prover 0: Proving ...
% 5.73/1.50  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.73/1.50  Prover 0: stopped
% 5.73/1.51  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.73/1.51  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.73/1.51  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.73/1.54  Prover 7: Preprocessing ...
% 5.73/1.55  Prover 8: Preprocessing ...
% 5.73/1.55  Prover 11: Preprocessing ...
% 5.73/1.56  Prover 10: Preprocessing ...
% 5.73/1.56  Prover 13: Preprocessing ...
% 5.73/1.56  Prover 1: Found proof (size 20)
% 5.73/1.56  Prover 1: proved (922ms)
% 5.73/1.56  Prover 4: stopped
% 5.73/1.57  Prover 10: stopped
% 5.73/1.57  Prover 13: stopped
% 5.73/1.57  Prover 7: Warning: ignoring some quantifiers
% 5.73/1.58  Prover 7: Constructing countermodel ...
% 6.40/1.59  Prover 7: stopped
% 6.40/1.59  Prover 11: stopped
% 6.40/1.61  Prover 8: Warning: ignoring some quantifiers
% 6.40/1.62  Prover 8: Constructing countermodel ...
% 6.40/1.62  Prover 8: stopped
% 6.40/1.62  
% 6.40/1.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.40/1.62  
% 6.40/1.63  % SZS output start Proof for theBenchmark
% 6.40/1.63  Assumptions after simplification:
% 6.40/1.63  ---------------------------------
% 6.40/1.63  
% 6.40/1.63    (con)
% 6.40/1.67     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: any] :  ? [v5:
% 6.40/1.67      any] : (line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 &
% 6.40/1.67      distinct_points(v2, v1) = v5 & distinct_points(v2, v0) = v4 &
% 6.40/1.67      distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 =
% 6.40/1.67          0) |  ~ (v4 = 0)))
% 6.40/1.67  
% 6.40/1.67    (con1)
% 6.40/1.67     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 6.40/1.67      (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ~
% 6.40/1.67      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] :  ? [v6: any]
% 6.40/1.67      : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 6.40/1.67        distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 6.40/1.67  
% 6.40/1.67    (function-axioms)
% 6.40/1.68     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.40/1.68      (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) & 
% 6.40/1.68    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.40/1.68      (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  !
% 6.40/1.68    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 6.40/1.68      $i] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~
% 6.40/1.68      (apart_point_and_line(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 6.40/1.68      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.40/1.68      (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  !
% 6.40/1.68    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 6.40/1.68      $i] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3,
% 6.40/1.68          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 6.40/1.68    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 6.40/1.68      (distinct_points(v3, v2) = v0))
% 6.40/1.68  
% 6.40/1.68  Further assumptions not needed in the proof:
% 6.40/1.68  --------------------------------------------
% 6.40/1.68  apart1, apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con2, cu1
% 6.40/1.68  
% 6.40/1.68  Those formulas are unsatisfiable:
% 6.40/1.68  ---------------------------------
% 6.40/1.68  
% 6.40/1.68  Begin of proof
% 6.40/1.68  | 
% 6.40/1.68  | ALPHA: (function-axioms) implies:
% 6.40/1.68  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 6.40/1.68  |         ! [v3: $i] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~
% 6.40/1.68  |          (distinct_points(v3, v2) = v0))
% 6.40/1.68  | 
% 6.40/1.68  | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 6.40/1.68  |        all_15_3, all_15_4, all_15_5 gives:
% 6.40/1.69  |   (2)  line_connecting(all_15_5, all_15_4) = all_15_2 &
% 6.40/1.69  |        apart_point_and_line(all_15_3, all_15_2) = 0 &
% 6.40/1.69  |        distinct_points(all_15_3, all_15_4) = all_15_0 &
% 6.40/1.69  |        distinct_points(all_15_3, all_15_5) = all_15_1 &
% 6.40/1.69  |        distinct_points(all_15_5, all_15_4) = 0 & $i(all_15_2) & $i(all_15_3) &
% 6.40/1.69  |        $i(all_15_4) & $i(all_15_5) & ( ~ (all_15_0 = 0) |  ~ (all_15_1 = 0))
% 6.40/1.69  | 
% 6.40/1.69  | ALPHA: (2) implies:
% 6.40/1.69  |   (3)  $i(all_15_5)
% 6.40/1.69  |   (4)  $i(all_15_4)
% 6.40/1.69  |   (5)  $i(all_15_3)
% 6.40/1.69  |   (6)  distinct_points(all_15_5, all_15_4) = 0
% 6.40/1.69  |   (7)  distinct_points(all_15_3, all_15_5) = all_15_1
% 6.40/1.69  |   (8)  distinct_points(all_15_3, all_15_4) = all_15_0
% 6.40/1.69  |   (9)  apart_point_and_line(all_15_3, all_15_2) = 0
% 6.40/1.69  |   (10)  line_connecting(all_15_5, all_15_4) = all_15_2
% 6.40/1.69  |   (11)   ~ (all_15_0 = 0) |  ~ (all_15_1 = 0)
% 6.40/1.69  | 
% 6.40/1.69  | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_3, all_15_2,
% 6.40/1.69  |              simplifying with (3), (4), (5), (9), (10) gives:
% 6.40/1.69  |   (12)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 6.40/1.69  |         (distinct_points(all_15_3, all_15_4) = v2 & distinct_points(all_15_3,
% 6.40/1.69  |             all_15_5) = v1 & distinct_points(all_15_5, all_15_4) = v0 & ( ~
% 6.40/1.69  |             (v0 = 0) | (v2 = 0 & v1 = 0)))
% 6.40/1.69  | 
% 6.40/1.69  | DELTA: instantiating (12) with fresh symbols all_22_0, all_22_1, all_22_2
% 6.40/1.69  |        gives:
% 6.40/1.69  |   (13)  distinct_points(all_15_3, all_15_4) = all_22_0 &
% 6.40/1.69  |         distinct_points(all_15_3, all_15_5) = all_22_1 &
% 6.40/1.69  |         distinct_points(all_15_5, all_15_4) = all_22_2 & ( ~ (all_22_2 = 0) |
% 6.40/1.69  |           (all_22_0 = 0 & all_22_1 = 0))
% 6.40/1.69  | 
% 6.40/1.69  | ALPHA: (13) implies:
% 6.40/1.70  |   (14)  distinct_points(all_15_5, all_15_4) = all_22_2
% 6.40/1.70  |   (15)  distinct_points(all_15_3, all_15_5) = all_22_1
% 6.40/1.70  |   (16)  distinct_points(all_15_3, all_15_4) = all_22_0
% 6.40/1.70  |   (17)   ~ (all_22_2 = 0) | (all_22_0 = 0 & all_22_1 = 0)
% 6.40/1.70  | 
% 6.40/1.70  | GROUND_INST: instantiating (1) with 0, all_22_2, all_15_4, all_15_5,
% 6.40/1.70  |              simplifying with (6), (14) gives:
% 6.40/1.70  |   (18)  all_22_2 = 0
% 6.40/1.70  | 
% 6.40/1.70  | GROUND_INST: instantiating (1) with all_15_1, all_22_1, all_15_5, all_15_3,
% 6.40/1.70  |              simplifying with (7), (15) gives:
% 6.40/1.70  |   (19)  all_22_1 = all_15_1
% 6.40/1.70  | 
% 6.40/1.70  | GROUND_INST: instantiating (1) with all_15_0, all_22_0, all_15_4, all_15_3,
% 6.40/1.70  |              simplifying with (8), (16) gives:
% 6.40/1.70  |   (20)  all_22_0 = all_15_0
% 6.40/1.70  | 
% 6.40/1.70  | BETA: splitting (17) gives:
% 6.40/1.70  | 
% 6.40/1.70  | Case 1:
% 6.40/1.70  | | 
% 6.40/1.70  | |   (21)   ~ (all_22_2 = 0)
% 6.40/1.70  | | 
% 6.40/1.70  | | REDUCE: (18), (21) imply:
% 6.40/1.70  | |   (22)  $false
% 6.40/1.70  | | 
% 6.40/1.70  | | CLOSE: (22) is inconsistent.
% 6.40/1.70  | | 
% 6.40/1.70  | Case 2:
% 6.40/1.70  | | 
% 6.40/1.70  | |   (23)  all_22_0 = 0 & all_22_1 = 0
% 6.40/1.70  | | 
% 6.40/1.70  | | ALPHA: (23) implies:
% 6.40/1.70  | |   (24)  all_22_1 = 0
% 6.40/1.70  | |   (25)  all_22_0 = 0
% 6.40/1.70  | | 
% 6.40/1.70  | | COMBINE_EQS: (20), (25) imply:
% 6.40/1.70  | |   (26)  all_15_0 = 0
% 6.40/1.70  | | 
% 6.40/1.70  | | COMBINE_EQS: (19), (24) imply:
% 6.40/1.70  | |   (27)  all_15_1 = 0
% 6.40/1.70  | | 
% 6.40/1.70  | | BETA: splitting (11) gives:
% 6.40/1.70  | | 
% 6.40/1.70  | | Case 1:
% 6.40/1.70  | | | 
% 6.40/1.70  | | |   (28)   ~ (all_15_0 = 0)
% 6.40/1.70  | | | 
% 6.40/1.70  | | | REDUCE: (26), (28) imply:
% 6.40/1.70  | | |   (29)  $false
% 6.40/1.70  | | | 
% 6.40/1.71  | | | CLOSE: (29) is inconsistent.
% 6.40/1.71  | | | 
% 6.40/1.71  | | Case 2:
% 6.40/1.71  | | | 
% 6.40/1.71  | | |   (30)   ~ (all_15_1 = 0)
% 6.40/1.71  | | | 
% 6.40/1.71  | | | REDUCE: (27), (30) imply:
% 6.40/1.71  | | |   (31)  $false
% 6.40/1.71  | | | 
% 6.40/1.71  | | | CLOSE: (31) is inconsistent.
% 6.40/1.71  | | | 
% 6.40/1.71  | | End of split
% 6.40/1.71  | | 
% 6.40/1.71  | End of split
% 6.40/1.71  | 
% 6.40/1.71  End of proof
% 6.40/1.71  % SZS output end Proof for theBenchmark
% 6.40/1.71  
% 6.40/1.71  1087ms
%------------------------------------------------------------------------------