TSTP Solution File: KLE089+1 by Princess---170717
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%------------------------------------------------------------------------------
% 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
% Comments :
%------------------------------------------------------------------------------
%----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 Rümmer, 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 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.06/0.43
% 0.06/0.43 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 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
% 5.90/2.27 (additive_associativity)
% 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 (additive_commutativity)
% 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 (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 6.19/2.30
% 6.19/2.30 (additive_idempotence)
% 6.19/2.30 ! [v0: $int] : ! [v1: $int] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 6.19/2.30
% 6.19/2.30 (additive_identity)
% 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 | (13) addition(all_37_0, all_21_1) = all_21_1 & addition(all_21_2, all_21_2)
% 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
%------------------------------------------------------------------------------