## TSTP Solution File: KLE089+1 by Princess---170717

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Princess---170717
% Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess-casc +printProof -timeout=%d %s

% Computer : n039.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-514.6.1.el7.x86_64
% CPULimit : 300s
% DateTime : Fri Aug 18 16:44:47 EDT 2017

% Result   : Theorem 3.48s
% Output   : Proof 6.36s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KLE089+1 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : princess-casc +printProof -timeout=%d %s
% 0.03/0.22  % Computer : n039.star.cs.uiowa.edu
% 0.03/0.22  % Model    : x86_64 x86_64
% 0.03/0.22  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.22  % Memory   : 32218.625MB
% 0.03/0.22  % OS       : Linux 3.10.0-514.6.1.el7.x86_64
% 0.03/0.22  % CPULimit : 300
% 0.03/0.22  % DateTime : Tue Aug 15 15:58:56 CDT 2017
% 0.03/0.22  % CPUTime  :
% 0.06/0.43  ________       _____
% 0.06/0.43  ___  __ \_________(_)________________________________
% 0.06/0.43  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.06/0.43  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.06/0.43  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.06/0.43
% 0.06/0.43  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.06/0.43  (CASC 2017-07-17)
% 0.06/0.43
% 0.06/0.43  (c) Philipp RÃ¼mmer, 2009-2017
% 0.06/0.43  (contributions by Peter Backeman, Peter Baumgartner,
% 0.06/0.43                    Angelo Brillout, Aleksandar Zeljic)
% 0.06/0.43  Free software under GNU Lesser General Public License (LGPL).
% 0.06/0.43  Bug reports to ph_r@gmx.net
% 0.06/0.43
% 0.06/0.43
% 0.06/0.46  Prover 0: Options:  +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off
% 1.21/0.80  Prover 0: Preprocessing ...
% 2.33/1.18  Prover 0: Proving ...
% 3.48/1.54  Prover 0: proved (1087ms)
% 3.48/1.54
% 3.48/1.54  VALID
% 3.48/1.54  % SZS status Theorem for theBenchmark
% 3.48/1.54
% 3.48/1.54  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 3.70/1.59  Prover 1: Preprocessing ...
% 4.00/1.67  Prover 1: Constructing countermodel ...
% 4.19/1.75  Prover 1: gave up
% 4.19/1.76  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off
% 4.19/1.79  Prover 4: Preprocessing ...
% 4.72/1.90  Prover 4: Constructing countermodel ...
% 5.90/2.25  Prover 4: Found proof (size 41)
% 5.90/2.25  Prover 4: proved (495ms)
% 5.90/2.25
% 5.90/2.25
% 5.90/2.26  % SZS output start Proof for theBenchmark
% 5.90/2.27  Assumptions after simplification:
% 5.90/2.27  ---------------------------------
% 5.90/2.27
% 6.19/2.30     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4: \$int]
% 6.19/2.30  : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5: \$int] :
% 6.19/2.30      (addition(v2, v5) = v4 & addition(v1, v0) = v5)) &  ! [v0: \$int] :  ! [v1:
% 6.19/2.30      \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4: \$int] : ( ~ (addition(v2,
% 6.19/2.30          v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5: \$int] : (addition(v5,
% 6.19/2.30          v0) = v4 & addition(v2, v1) = v5))
% 6.19/2.30
% 6.19/2.30     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] : ( ~ (addition(v1, v0) = v2) |
% 6.19/2.30      addition(v0, v1) = v2) &  ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] : ( ~
% 6.19/2.30
% 6.19/2.30     ! [v0: \$int] :  ! [v1: \$int] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 6.19/2.30
% 6.19/2.30     ! [v0: \$int] :  ! [v1: \$int] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 6.19/2.30
% 6.19/2.30    (domain1)
% 6.19/2.30     ! [v0: \$int] :  ! [v1: \$int] : ( ~ (antidomain(v0) = v1) | multiplication(v1,
% 6.19/2.30        v0) = zero)
% 6.19/2.30
% 6.19/2.30    (goals)
% 6.19/2.30     ? [v0: \$int] :  ? [v1: \$int] :  ? [v2: \$int] :  ? [v3: \$int] :  ? [v4: \$int]
% 6.19/2.30  : ( ~ (v4 = zero) & domain(v0) = v2 & antidomain(v1) = v3 & multiplication(v2,
% 6.19/2.30        v1) = v4 & addition(v2, v3) = v3)
% 6.19/2.30
% 6.19/2.30    (left_distributivity)
% 6.19/2.31     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4: \$int]
% 6.19/2.31  :  ! [v5: \$int] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0,
% 6.19/2.31          v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6: \$int] :
% 6.19/2.31      (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) &  ! [v0: \$int] :  !
% 6.19/2.31    [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4: \$int] : ( ~
% 6.19/2.31      (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5: \$int] :
% 6.19/2.31       ? [v6: \$int] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 &
% 6.19/2.31        addition(v5, v6) = v4))
% 6.19/2.31
% 6.19/2.31    (axioms)
% 6.28/2.32     ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] : (v1 = v0 |  ~
% 6.28/2.32      (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int]
% 6.28/2.32  :  ! [v2: \$int] :  ! [v3: \$int] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1)
% 6.28/2.32      |  ~ (multiplication(v3, v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int] :  !
% 6.28/2.32    [v2: \$int] :  ! [v3: \$int] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~
% 6.28/2.32      (addition(v3, v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :
% 6.28/2.32    (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0)) &  ! [v0: \$int] :
% 6.28/2.32    ! [v1: \$int] :  ! [v2: \$int] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~
% 6.28/2.32      (coantidomain(v2) = v0)) &  ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :
% 6.28/2.32    (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0: \$int] :  !
% 6.28/2.32    [v1: \$int] :  ! [v2: \$int] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~
% 6.28/2.32      (antidomain(v2) = v0))
% 6.28/2.32
% 6.28/2.32  Further assumptions not needed in the proof:
% 6.28/2.32  --------------------------------------------
% 6.28/2.32  codomain1, codomain2, codomain3, codomain4, domain2, domain3, domain4,
% 6.28/2.32  left_annihilation, multiplicative_associativity, multiplicative_left_identity,
% 6.28/2.32  multiplicative_right_identity, order, right_annihilation, right_distributivity
% 6.28/2.32
% 6.28/2.32  Those formulas are unsatisfiable:
% 6.28/2.32  ---------------------------------
% 6.28/2.32
% 6.28/2.32  Begin of proof
% 6.28/2.32  |
% 6.28/2.32  | ALPHA: (additive_commutativity) implies:
% 6.28/2.32  |   (1)   ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] : ( ~ (addition(v1, v0) =
% 6.28/2.32  |            v2) | addition(v0, v1) = v2)
% 6.28/2.32  |
% 6.28/2.32  | ALPHA: (additive_associativity) implies:
% 6.28/2.32  |   (2)   ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4:
% 6.28/2.32  |          \$int] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ?
% 6.28/2.32  |          [v5: \$int] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 6.28/2.32  |
% 6.28/2.32  | ALPHA: (left_distributivity) implies:
% 6.28/2.32  |   (3)   ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] :  ! [v4:
% 6.28/2.32  |          \$int] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) =
% 6.28/2.32  |            v3) |  ? [v5: \$int] :  ? [v6: \$int] : (multiplication(v1, v2) = v6
% 6.28/2.32  |            & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 6.28/2.32  |
% 6.28/2.32  | ALPHA: (axioms) implies:
% 6.28/2.33  |   (4)   ! [v0: \$int] :  ! [v1: \$int] :  ! [v2: \$int] :  ! [v3: \$int] : (v1 =
% 6.28/2.33  |          v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) =
% 6.28/2.33  |            v0))
% 6.28/2.33  |
% 6.28/2.33  | DELTA: instantiating (goals) with fresh symbols all_21_0, all_21_1, all_21_2,
% 6.28/2.33  |        all_21_3, all_21_4 gives:
% 6.28/2.33  |   (5)   ~ (all_21_0 = zero) & domain(all_21_4) = all_21_2 &
% 6.28/2.33  |        antidomain(all_21_3) = all_21_1 & multiplication(all_21_2, all_21_3) =
% 6.28/2.33  |        all_21_0 & addition(all_21_2, all_21_1) = all_21_1
% 6.28/2.33  |
% 6.28/2.33  | ALPHA: (5) implies:
% 6.28/2.33  |   (6)   ~ (all_21_0 = zero)
% 6.28/2.33  |   (7)  addition(all_21_2, all_21_1) = all_21_1
% 6.28/2.33  |   (8)  multiplication(all_21_2, all_21_3) = all_21_0
% 6.28/2.33  |   (9)  antidomain(all_21_3) = all_21_1
% 6.28/2.33  |
% 6.28/2.33  | GROUND_INST: instantiating (domain1) with all_21_3, all_21_1, simplifying with
% 6.28/2.33  |              (9) gives:
% 6.28/2.33  |   (10)  multiplication(all_21_1, all_21_3) = zero
% 6.28/2.33  |
% 6.36/2.34  | GROUND_INST: instantiating (2) with all_21_1, all_21_2, all_21_2, all_21_1,
% 6.36/2.34  |              all_21_1, simplifying with (7) gives:
% 6.36/2.34  |   (11)   ? [v0: \$int] : (addition(v0, all_21_1) = all_21_1 &
% 6.36/2.34  |           addition(all_21_2, all_21_2) = v0)
% 6.36/2.34  |
% 6.36/2.34  | GROUND_INST: instantiating (1) with all_21_1, all_21_2, all_21_1, simplifying
% 6.36/2.34  |              with (7) gives:
% 6.36/2.34  |   (12)  addition(all_21_1, all_21_2) = all_21_1
% 6.36/2.34  |
% 6.36/2.34  | DELTA: instantiating (11) with fresh symbol all_37_0 gives:
% 6.36/2.34  |         = all_37_0
% 6.36/2.34  |
% 6.36/2.34  | ALPHA: (13) implies:
% 6.36/2.34  |   (14)  addition(all_21_2, all_21_2) = all_37_0
% 6.36/2.34  |   (15)  addition(all_37_0, all_21_1) = all_21_1
% 6.36/2.34  |
% 6.36/2.34  | GROUND_INST: instantiating (additive_idempotence) with all_21_2, all_37_0,
% 6.36/2.34  |              simplifying with (14) gives:
% 6.36/2.34  |   (16)  all_37_0 = all_21_2
% 6.36/2.34  |
% 6.36/2.34  | REDUCE: (14), (16) imply:
% 6.36/2.34  |   (17)  addition(all_21_2, all_21_2) = all_21_2
% 6.36/2.34  |
% 6.36/2.34  | GROUND_INST: instantiating (3) with all_21_2, all_21_1, all_21_3, all_21_1,
% 6.36/2.34  |              zero, simplifying with (7), (10) gives:
% 6.36/2.34  |   (18)   ? [v0: \$int] :  ? [v1: \$int] : (multiplication(all_21_1, all_21_3) =
% 6.36/2.34  |           v1 & multiplication(all_21_2, all_21_3) = v0 & addition(v0, v1) =
% 6.36/2.34  |           zero)
% 6.36/2.34  |
% 6.36/2.34  | GROUND_INST: instantiating (3) with all_21_1, all_21_2, all_21_3, all_21_1,
% 6.36/2.34  |              zero, simplifying with (10), (12) gives:
% 6.36/2.34  |   (19)   ? [v0: \$int] :  ? [v1: \$int] : (multiplication(all_21_1, all_21_3) =
% 6.36/2.34  |           v0 & multiplication(all_21_2, all_21_3) = v1 & addition(v0, v1) =
% 6.36/2.34  |           zero)
% 6.36/2.34  |
% 6.36/2.34  | GROUND_INST: instantiating (3) with all_21_2, all_21_2, all_21_3, all_21_2,
% 6.36/2.34  |              all_21_0, simplifying with (8), (17) gives:
% 6.36/2.34  |   (20)   ? [v0: \$int] :  ? [v1: \$int] : (multiplication(all_21_2, all_21_3) =
% 6.36/2.34  |           v1 & multiplication(all_21_2, all_21_3) = v0 & addition(v0, v1) =
% 6.36/2.34  |           all_21_0)
% 6.36/2.34  |
% 6.36/2.34  | DELTA: instantiating (20) with fresh symbols all_59_0, all_59_1 gives:
% 6.36/2.34  |   (21)  multiplication(all_21_2, all_21_3) = all_59_0 &
% 6.36/2.34  |         multiplication(all_21_2, all_21_3) = all_59_1 & addition(all_59_1,
% 6.36/2.34  |           all_59_0) = all_21_0
% 6.36/2.34  |
% 6.36/2.34  | ALPHA: (21) implies:
% 6.36/2.34  |   (22)  multiplication(all_21_2, all_21_3) = all_59_1
% 6.36/2.34  |   (23)  multiplication(all_21_2, all_21_3) = all_59_0
% 6.36/2.34  |
% 6.36/2.34  | DELTA: instantiating (18) with fresh symbols all_73_0, all_73_1 gives:
% 6.36/2.34  |   (24)  multiplication(all_21_1, all_21_3) = all_73_0 &
% 6.36/2.34  |         multiplication(all_21_2, all_21_3) = all_73_1 & addition(all_73_1,
% 6.36/2.34  |           all_73_0) = zero
% 6.36/2.34  |
% 6.36/2.34  | ALPHA: (24) implies:
% 6.36/2.34  |   (25)  addition(all_73_1, all_73_0) = zero
% 6.36/2.34  |   (26)  multiplication(all_21_2, all_21_3) = all_73_1
% 6.36/2.34  |   (27)  multiplication(all_21_1, all_21_3) = all_73_0
% 6.36/2.34  |
% 6.36/2.34  | DELTA: instantiating (19) with fresh symbols all_89_0, all_89_1 gives:
% 6.36/2.35  |   (28)  multiplication(all_21_1, all_21_3) = all_89_1 &
% 6.36/2.35  |         multiplication(all_21_2, all_21_3) = all_89_0 & addition(all_89_1,
% 6.36/2.35  |           all_89_0) = zero
% 6.36/2.35  |
% 6.36/2.35  | ALPHA: (28) implies:
% 6.36/2.35  |   (29)  multiplication(all_21_2, all_21_3) = all_89_0
% 6.36/2.35  |   (30)  multiplication(all_21_1, all_21_3) = all_89_1
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with zero, all_89_1, all_21_3, all_21_1,
% 6.36/2.35  |              simplifying with (10), (30) gives:
% 6.36/2.35  |   (31)  all_89_1 = zero
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with all_89_1, all_73_0, all_21_3, all_21_1,
% 6.36/2.35  |              simplifying with (27), (30) gives:
% 6.36/2.35  |   (32)  all_89_1 = all_73_0
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with all_21_0, all_73_1, all_21_3, all_21_2,
% 6.36/2.35  |              simplifying with (8), (26) gives:
% 6.36/2.35  |   (33)  all_73_1 = all_21_0
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with all_89_0, all_73_1, all_21_3, all_21_2,
% 6.36/2.35  |              simplifying with (26), (29) gives:
% 6.36/2.35  |   (34)  all_89_0 = all_73_1
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with all_73_1, all_59_0, all_21_3, all_21_2,
% 6.36/2.35  |              simplifying with (23), (26) gives:
% 6.36/2.35  |   (35)  all_73_1 = all_59_0
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (4) with all_89_0, all_59_1, all_21_3, all_21_2,
% 6.36/2.35  |              simplifying with (22), (29) gives:
% 6.36/2.35  |   (36)  all_89_0 = all_59_1
% 6.36/2.35  |
% 6.36/2.35  | COMBINE_EQS: (34), (36) imply:
% 6.36/2.35  |   (37)  all_73_1 = all_59_1
% 6.36/2.35  |
% 6.36/2.35  | SIMP: (37) implies:
% 6.36/2.35  |   (38)  all_73_1 = all_59_1
% 6.36/2.35  |
% 6.36/2.35  | COMBINE_EQS: (31), (32) imply:
% 6.36/2.35  |   (39)  all_73_0 = zero
% 6.36/2.35  |
% 6.36/2.35  | COMBINE_EQS: (33), (35) imply:
% 6.36/2.35  |   (40)  all_59_0 = all_21_0
% 6.36/2.35  |
% 6.36/2.35  | COMBINE_EQS: (35), (38) imply:
% 6.36/2.35  |   (41)  all_59_0 = all_59_1
% 6.36/2.35  |
% 6.36/2.35  | COMBINE_EQS: (40), (41) imply:
% 6.36/2.35  |   (42)  all_59_1 = all_21_0
% 6.36/2.35  |
% 6.36/2.35  | REDUCE: (25), (33), (39) imply:
% 6.36/2.35  |   (43)  addition(all_21_0, zero) = zero
% 6.36/2.35  |
% 6.36/2.35  | GROUND_INST: instantiating (additive_identity) with all_21_0, zero,
% 6.36/2.35  |              simplifying with (43) gives:
% 6.36/2.35  |   (44)  all_21_0 = zero
% 6.36/2.35  |
% 6.36/2.35  | REDUCE: (6), (44) imply:
% 6.36/2.35  |   (45)   ~ (0 = 0)
% 6.36/2.36  |
% 6.36/2.36  | CLOSE: (45) is inconsistent.
% 6.36/2.36  |
% 6.36/2.36  End of proof
% 6.36/2.36  % SZS output end Proof for theBenchmark
% 6.36/2.36
% 6.36/2.36  1922ms
%------------------------------------------------------------------------------
```