TSTP Solution File: KRS003_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS003_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n015.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 : Thu Aug 31 05:50:58 EDT 2023

% Result   : Theorem 5.67s 1.55s
% Output   : Proof 7.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS003_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Aug 28 02:24:09 EDT 2023
% 0.14/0.34  % 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/sandbox2/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 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 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 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
% 2.33/1.06  Prover 1: Preprocessing ...
% 2.33/1.07  Prover 4: Preprocessing ...
% 2.83/1.11  Prover 5: Preprocessing ...
% 2.83/1.11  Prover 3: Preprocessing ...
% 2.83/1.11  Prover 0: Preprocessing ...
% 2.83/1.11  Prover 2: Preprocessing ...
% 2.83/1.11  Prover 6: Preprocessing ...
% 3.76/1.35  Prover 2: Proving ...
% 3.76/1.35  Prover 5: Proving ...
% 3.76/1.37  Prover 1: Constructing countermodel ...
% 3.76/1.37  Prover 6: Constructing countermodel ...
% 3.76/1.39  Prover 3: Constructing countermodel ...
% 5.09/1.44  Prover 0: Proving ...
% 5.09/1.45  Prover 4: Constructing countermodel ...
% 5.09/1.50  Prover 6: gave up
% 5.09/1.50  Prover 3: gave up
% 5.09/1.50  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.09/1.50  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.67/1.53  Prover 7: Preprocessing ...
% 5.67/1.53  Prover 1: gave up
% 5.67/1.53  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.67/1.55  Prover 2: proved (906ms)
% 5.67/1.55  Prover 5: proved (904ms)
% 5.67/1.55  
% 5.67/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55  
% 5.67/1.55  Prover 8: Preprocessing ...
% 5.67/1.55  
% 5.67/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55  
% 5.67/1.55  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.67/1.55  Prover 0: stopped
% 5.67/1.56  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.67/1.56  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.67/1.57  Prover 9: Preprocessing ...
% 6.19/1.59  Prover 10: Preprocessing ...
% 6.19/1.59  Prover 13: Preprocessing ...
% 6.19/1.61  Prover 11: Preprocessing ...
% 6.19/1.61  Prover 7: Constructing countermodel ...
% 6.19/1.62  Prover 13: Warning: ignoring some quantifiers
% 6.19/1.63  Prover 7: gave up
% 6.19/1.63  Prover 13: Constructing countermodel ...
% 6.19/1.64  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.19/1.64  Prover 10: Constructing countermodel ...
% 6.19/1.65  Prover 8: Warning: ignoring some quantifiers
% 6.19/1.66  Prover 8: Constructing countermodel ...
% 6.19/1.66  Prover 10: gave up
% 6.19/1.67  Prover 16: Preprocessing ...
% 6.86/1.69  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.97/1.69  Prover 16: Warning: ignoring some quantifiers
% 6.97/1.70  Prover 16: Constructing countermodel ...
% 7.14/1.72  Prover 19: Preprocessing ...
% 7.23/1.73  Prover 9: Constructing countermodel ...
% 7.23/1.73  Prover 8: gave up
% 7.23/1.73  Prover 9: stopped
% 7.23/1.74  Prover 13: Found proof (size 25)
% 7.23/1.74  Prover 13: proved (179ms)
% 7.23/1.74  Prover 4: stopped
% 7.23/1.74  Prover 16: stopped
% 7.23/1.77  Prover 11: Constructing countermodel ...
% 7.23/1.77  Prover 19: Warning: ignoring some quantifiers
% 7.23/1.78  Prover 19: Constructing countermodel ...
% 7.23/1.79  Prover 19: stopped
% 7.23/1.79  Prover 11: stopped
% 7.23/1.79  
% 7.23/1.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.23/1.79  
% 7.23/1.79  % SZS output start Proof for theBenchmark
% 7.23/1.80  Assumptions after simplification:
% 7.23/1.80  ---------------------------------
% 7.23/1.80  
% 7.23/1.80    (clause_11)
% 7.23/1.80     ! [v0: real] :  ! [v1: real] :  ! [v2: unreal] : ( ~ real(v1) |  ~ real(v0) |
% 7.23/1.80       ~ unreal(v2) |  ~ s(v2, v1) |  ~ s(v2, v0) |  ~ s1most(v2) | equalish(v1,
% 7.23/1.80        v0))
% 7.23/1.80  
% 7.23/1.80    (clause_15)
% 7.23/1.80     ! [v0: unreal] : ( ~ unreal(v0) |  ~ e(v0) | c(v0))
% 7.23/1.80  
% 7.23/1.80    (clause_16)
% 7.23/1.80     ! [v0: unreal] : ( ~ unreal(v0) |  ~ f(v0) | d(v0))
% 7.23/1.80  
% 7.23/1.80    (clause_1__clause_2)
% 7.23/1.80    unreal(exist) & e(exist) & f(exist)
% 7.23/1.80  
% 7.23/1.80    (clause_3)
% 7.23/1.80     ! [v0: unreal] : ( ~ unreal(v0) |  ~ c(v0) | s2least(v0))
% 7.23/1.80  
% 7.23/1.80    (clause_5)
% 7.75/1.83     ! [v0: unreal] :  ! [v1: real] : ( ~ (u1r2(v0) = v1) |  ~ unreal(v0) |  ~
% 7.75/1.83      s2least(v0) |  ? [v2: real] : (u1r1(v0) = v2 & real(v2) &  ~ equalish(v1,
% 7.75/1.83          v2))) &  ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0) |  ? [v1:
% 7.75/1.83        real] :  ? [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) &
% 7.75/1.83        real(v1) &  ~ equalish(v1, v2)))
% 7.75/1.83  
% 7.75/1.83    (clause_6)
% 7.75/1.83     ! [v0: unreal] :  ! [v1: real] : ( ~ (u1r1(v0) = v1) |  ~ unreal(v0) |  ~
% 7.75/1.83      s2least(v0) | s(v0, v1)) &  ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0)
% 7.75/1.83      |  ? [v1: real] : (u1r1(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.83  
% 7.75/1.83    (clause_7)
% 7.75/1.83     ! [v0: unreal] :  ! [v1: real] : ( ~ (u1r2(v0) = v1) |  ~ unreal(v0) |  ~
% 7.75/1.83      s2least(v0) | s(v0, v1)) &  ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0)
% 7.75/1.83      |  ? [v1: real] : (u1r2(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.83  
% 7.75/1.83    (clause_9)
% 7.75/1.83     ! [v0: unreal] : ( ~ unreal(v0) |  ~ d(v0) | s1most(v0))
% 7.75/1.83  
% 7.75/1.83    (function-axioms)
% 7.75/1.84     ! [v0: real] :  ! [v1: real] :  ! [v2: unreal] : (v1 = v0 |  ~ (u3r2(v2) =
% 7.75/1.84        v1) |  ~ (u3r2(v2) = v0)) &  ! [v0: real] :  ! [v1: real] :  ! [v2:
% 7.75/1.84      unreal] : (v1 = v0 |  ~ (u3r1(v2) = v1) |  ~ (u3r1(v2) = v0)) &  ! [v0:
% 7.75/1.84      real] :  ! [v1: real] :  ! [v2: unreal] : (v1 = v0 |  ~ (u1r2(v2) = v1) |  ~
% 7.75/1.84      (u1r2(v2) = v0)) &  ! [v0: real] :  ! [v1: real] :  ! [v2: unreal] : (v1 =
% 7.75/1.84      v0 |  ~ (u1r1(v2) = v1) |  ~ (u1r1(v2) = v0))
% 7.75/1.84  
% 7.75/1.84  Further assumptions not needed in the proof:
% 7.75/1.84  --------------------------------------------
% 7.75/1.84  clause_10, clause_12, clause_13, clause_14, clause_4, clause_8
% 7.75/1.84  
% 7.75/1.84  Those formulas are unsatisfiable:
% 7.75/1.84  ---------------------------------
% 7.75/1.84  
% 7.75/1.84  Begin of proof
% 7.75/1.84  | 
% 7.75/1.84  | ALPHA: (clause_5) implies:
% 7.75/1.84  |   (1)   ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0) |  ? [v1: real] :  ?
% 7.75/1.84  |          [v2: real] : (u1r2(v0) = v1 & u1r1(v0) = v2 & real(v2) & real(v1) & 
% 7.75/1.84  |            ~ equalish(v1, v2)))
% 7.75/1.84  | 
% 7.75/1.84  | ALPHA: (clause_6) implies:
% 7.75/1.84  |   (2)   ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0) |  ? [v1: real] :
% 7.75/1.84  |          (u1r1(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.84  | 
% 7.75/1.84  | ALPHA: (clause_7) implies:
% 7.75/1.84  |   (3)   ! [v0: unreal] : ( ~ unreal(v0) |  ~ s2least(v0) |  ? [v1: real] :
% 7.75/1.84  |          (u1r2(v0) = v1 & real(v1) & s(v0, v1)))
% 7.75/1.84  | 
% 7.75/1.84  | ALPHA: (clause_1__clause_2) implies:
% 7.75/1.84  |   (4)  f(exist)
% 7.75/1.84  |   (5)  e(exist)
% 7.75/1.84  |   (6)  unreal(exist)
% 7.75/1.84  | 
% 7.75/1.84  | ALPHA: (function-axioms) implies:
% 7.75/1.84  |   (7)   ! [v0: real] :  ! [v1: real] :  ! [v2: unreal] : (v1 = v0 |  ~
% 7.75/1.84  |          (u1r1(v2) = v1) |  ~ (u1r1(v2) = v0))
% 7.75/1.85  |   (8)   ! [v0: real] :  ! [v1: real] :  ! [v2: unreal] : (v1 = v0 |  ~
% 7.75/1.85  |          (u1r2(v2) = v1) |  ~ (u1r2(v2) = v0))
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (clause_16) with exist, simplifying with (4), (6)
% 7.75/1.85  |              gives:
% 7.75/1.85  |   (9)  d(exist)
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (clause_15) with exist, simplifying with (5), (6)
% 7.75/1.85  |              gives:
% 7.75/1.85  |   (10)  c(exist)
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (clause_9) with exist, simplifying with (6), (9)
% 7.75/1.85  |              gives:
% 7.75/1.85  |   (11)  s1most(exist)
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (clause_3) with exist, simplifying with (6), (10)
% 7.75/1.85  |              gives:
% 7.75/1.85  |   (12)  s2least(exist)
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (1) with exist, simplifying with (6), (12) gives:
% 7.75/1.85  |   (13)   ? [v0: real] :  ? [v1: real] : (u1r2(exist) = v0 & u1r1(exist) = v1 &
% 7.75/1.85  |           real(v1) & real(v0) &  ~ equalish(v0, v1))
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (3) with exist, simplifying with (6), (12) gives:
% 7.75/1.85  |   (14)   ? [v0: real] : (u1r2(exist) = v0 & real(v0) & s(exist, v0))
% 7.75/1.85  | 
% 7.75/1.85  | GROUND_INST: instantiating (2) with exist, simplifying with (6), (12) gives:
% 7.75/1.85  |   (15)   ? [v0: real] : (u1r1(exist) = v0 & real(v0) & s(exist, v0))
% 7.75/1.85  | 
% 7.75/1.85  | DELTA: instantiating (15) with fresh symbol all_42_0 gives:
% 7.75/1.85  |   (16)  u1r1(exist) = all_42_0 & real(all_42_0) & s(exist, all_42_0)
% 7.75/1.85  | 
% 7.75/1.85  | ALPHA: (16) implies:
% 7.75/1.85  |   (17)  s(exist, all_42_0)
% 7.75/1.85  |   (18)  u1r1(exist) = all_42_0
% 7.75/1.85  | 
% 7.75/1.85  | DELTA: instantiating (14) with fresh symbol all_44_0 gives:
% 7.75/1.85  |   (19)  u1r2(exist) = all_44_0 & real(all_44_0) & s(exist, all_44_0)
% 7.75/1.85  | 
% 7.75/1.85  | ALPHA: (19) implies:
% 7.75/1.85  |   (20)  s(exist, all_44_0)
% 7.75/1.85  |   (21)  u1r2(exist) = all_44_0
% 7.75/1.85  | 
% 7.75/1.85  | DELTA: instantiating (13) with fresh symbols all_46_0, all_46_1 gives:
% 7.75/1.86  |   (22)  u1r2(exist) = all_46_1 & u1r1(exist) = all_46_0 & real(all_46_0) &
% 7.75/1.86  |         real(all_46_1) &  ~ equalish(all_46_1, all_46_0)
% 7.75/1.86  | 
% 7.75/1.86  | ALPHA: (22) implies:
% 7.75/1.86  |   (23)   ~ equalish(all_46_1, all_46_0)
% 7.75/1.86  |   (24)  real(all_46_1)
% 7.75/1.86  |   (25)  real(all_46_0)
% 7.75/1.86  |   (26)  u1r1(exist) = all_46_0
% 7.75/1.86  |   (27)  u1r2(exist) = all_46_1
% 7.75/1.86  | 
% 7.75/1.86  | GROUND_INST: instantiating (7) with all_42_0, all_46_0, exist, simplifying
% 7.75/1.86  |              with (18), (26) gives:
% 7.75/1.86  |   (28)  all_46_0 = all_42_0
% 7.75/1.86  | 
% 7.75/1.86  | GROUND_INST: instantiating (8) with all_44_0, all_46_1, exist, simplifying
% 7.75/1.86  |              with (21), (27) gives:
% 7.75/1.86  |   (29)  all_46_1 = all_44_0
% 7.75/1.86  | 
% 7.75/1.86  | REDUCE: (25), (28) imply:
% 7.75/1.86  |   (30)  real(all_42_0)
% 7.75/1.86  | 
% 7.75/1.86  | REDUCE: (24), (29) imply:
% 7.75/1.86  |   (31)  real(all_44_0)
% 7.75/1.86  | 
% 7.75/1.86  | REDUCE: (23), (28), (29) imply:
% 7.75/1.86  |   (32)   ~ equalish(all_44_0, all_42_0)
% 7.75/1.86  | 
% 7.75/1.86  | GROUND_INST: instantiating (clause_11) with all_42_0, all_44_0, exist,
% 7.75/1.86  |              simplifying with (6), (11), (17), (20), (30), (31), (32) gives:
% 7.75/1.86  |   (33)  $false
% 7.75/1.86  | 
% 7.75/1.86  | CLOSE: (33) is inconsistent.
% 7.75/1.86  | 
% 7.75/1.86  End of proof
% 7.75/1.86  % SZS output end Proof for theBenchmark
% 7.75/1.86  
% 7.75/1.86  1251ms
%------------------------------------------------------------------------------