TSTP Solution File: KLE001+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 05:34:08 EDT 2023
% Result : Theorem 5.46s 1.46s
% Output : Proof 6.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 12:34:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.63/0.62 ________ _____
% 0.63/0.62 ___ __ \_________(_)________________________________
% 0.63/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.63/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.63/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.63/0.62 (2023-06-19)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2023
% 0.63/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.63/0.62 Amanda Stjerna.
% 0.63/0.62 Free software under BSD-3-Clause.
% 0.63/0.62
% 0.63/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.63 Running up to 7 provers in parallel.
% 0.69/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.69/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.24/1.03 Prover 4: Preprocessing ...
% 2.24/1.03 Prover 1: Preprocessing ...
% 2.68/1.07 Prover 3: Preprocessing ...
% 2.68/1.07 Prover 5: Preprocessing ...
% 2.68/1.07 Prover 6: Preprocessing ...
% 2.68/1.07 Prover 0: Preprocessing ...
% 2.68/1.07 Prover 2: Preprocessing ...
% 3.99/1.30 Prover 1: Constructing countermodel ...
% 3.99/1.30 Prover 6: Constructing countermodel ...
% 3.99/1.30 Prover 3: Constructing countermodel ...
% 3.99/1.33 Prover 4: Constructing countermodel ...
% 4.66/1.34 Prover 5: Proving ...
% 4.66/1.35 Prover 0: Proving ...
% 5.04/1.44 Prover 2: Proving ...
% 5.46/1.46 Prover 3: proved (811ms)
% 5.46/1.46
% 5.46/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/1.46
% 5.46/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.53/1.46 Prover 6: stopped
% 5.53/1.46 Prover 0: stopped
% 5.53/1.46 Prover 2: stopped
% 5.53/1.47 Prover 5: stopped
% 5.53/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.53/1.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.53/1.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.53/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.53/1.49 Prover 10: Preprocessing ...
% 5.53/1.49 Prover 7: Preprocessing ...
% 5.53/1.49 Prover 8: Preprocessing ...
% 5.53/1.50 Prover 1: Found proof (size 14)
% 5.53/1.50 Prover 1: proved (854ms)
% 5.53/1.50 Prover 4: stopped
% 5.53/1.50 Prover 11: Preprocessing ...
% 5.89/1.51 Prover 10: stopped
% 5.89/1.51 Prover 7: stopped
% 5.89/1.52 Prover 13: Preprocessing ...
% 5.89/1.53 Prover 11: stopped
% 5.89/1.54 Prover 13: stopped
% 6.11/1.54 Prover 8: Warning: ignoring some quantifiers
% 6.11/1.55 Prover 8: Constructing countermodel ...
% 6.11/1.56 Prover 8: stopped
% 6.11/1.56
% 6.11/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.11/1.56
% 6.11/1.56 % SZS output start Proof for theBenchmark
% 6.11/1.56 Assumptions after simplification:
% 6.11/1.56 ---------------------------------
% 6.11/1.56
% 6.11/1.56 (additive_commutativity)
% 6.11/1.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (addition(v0, v1) = v2) | ~
% 6.11/1.59 $i(v1) | ~ $i(v0) | (addition(v1, v0) = v2 & $i(v2)))
% 6.11/1.59
% 6.11/1.59 (additive_idempotence)
% 6.11/1.60 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 6.11/1.60
% 6.11/1.60 (goals)
% 6.11/1.60 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 6.11/1.60 = 0) & leq(v3, v3) = v4 & leq(v0, v1) = 0 & addition(v0, v2) = v3 & $i(v3)
% 6.11/1.60 & $i(v2) & $i(v1) & $i(v0))
% 6.11/1.60
% 6.11/1.60 (order)
% 6.11/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = v2) |
% 6.11/1.60 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) & addition(v0, v1) = v3 &
% 6.11/1.60 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) |
% 6.11/1.60 ~ $i(v0) | addition(v0, v1) = v1)
% 6.11/1.60
% 6.11/1.60 Further assumptions not needed in the proof:
% 6.11/1.60 --------------------------------------------
% 6.11/1.60 additive_associativity, additive_identity, left_annihilation,
% 6.11/1.60 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 6.11/1.60 multiplicative_right_identity, right_annihilation, right_distributivity
% 6.11/1.60
% 6.11/1.60 Those formulas are unsatisfiable:
% 6.11/1.60 ---------------------------------
% 6.11/1.60
% 6.11/1.60 Begin of proof
% 6.11/1.60 |
% 6.11/1.60 | ALPHA: (order) implies:
% 6.11/1.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 6.11/1.61 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 6.11/1.61 | addition(v0, v1) = v3 & $i(v3)))
% 6.11/1.61 |
% 6.11/1.61 | DELTA: instantiating (goals) with fresh symbols all_16_0, all_16_1, all_16_2,
% 6.11/1.61 | all_16_3, all_16_4 gives:
% 6.11/1.61 | (2) ~ (all_16_0 = 0) & leq(all_16_1, all_16_1) = all_16_0 & leq(all_16_4,
% 6.11/1.61 | all_16_3) = 0 & addition(all_16_4, all_16_2) = all_16_1 &
% 6.11/1.61 | $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & $i(all_16_4)
% 6.11/1.61 |
% 6.11/1.61 | ALPHA: (2) implies:
% 6.11/1.61 | (3) ~ (all_16_0 = 0)
% 6.11/1.61 | (4) $i(all_16_4)
% 6.11/1.61 | (5) $i(all_16_2)
% 6.11/1.61 | (6) addition(all_16_4, all_16_2) = all_16_1
% 6.11/1.61 | (7) leq(all_16_1, all_16_1) = all_16_0
% 6.11/1.61 |
% 6.11/1.61 | GROUND_INST: instantiating (additive_commutativity) with all_16_4, all_16_2,
% 6.11/1.61 | all_16_1, simplifying with (4), (5), (6) gives:
% 6.11/1.61 | (8) addition(all_16_2, all_16_4) = all_16_1 & $i(all_16_1)
% 6.11/1.61 |
% 6.11/1.61 | ALPHA: (8) implies:
% 6.11/1.61 | (9) $i(all_16_1)
% 6.11/1.62 |
% 6.11/1.62 | GROUND_INST: instantiating (1) with all_16_1, all_16_1, all_16_0, simplifying
% 6.11/1.62 | with (7), (9) gives:
% 6.11/1.62 | (10) all_16_0 = 0 | ? [v0: any] : ( ~ (v0 = all_16_1) & addition(all_16_1,
% 6.11/1.62 | all_16_1) = v0 & $i(v0))
% 6.11/1.62 |
% 6.11/1.62 | BETA: splitting (10) gives:
% 6.11/1.62 |
% 6.11/1.62 | Case 1:
% 6.11/1.62 | |
% 6.11/1.62 | | (11) all_16_0 = 0
% 6.11/1.62 | |
% 6.11/1.62 | | REDUCE: (3), (11) imply:
% 6.11/1.62 | | (12) $false
% 6.11/1.62 | |
% 6.11/1.62 | | CLOSE: (12) is inconsistent.
% 6.11/1.62 | |
% 6.11/1.62 | Case 2:
% 6.11/1.62 | |
% 6.11/1.62 | | (13) ? [v0: any] : ( ~ (v0 = all_16_1) & addition(all_16_1, all_16_1) =
% 6.11/1.62 | | v0 & $i(v0))
% 6.11/1.62 | |
% 6.11/1.62 | | DELTA: instantiating (13) with fresh symbol all_28_0 gives:
% 6.11/1.62 | | (14) ~ (all_28_0 = all_16_1) & addition(all_16_1, all_16_1) = all_28_0 &
% 6.11/1.62 | | $i(all_28_0)
% 6.11/1.62 | |
% 6.11/1.62 | | ALPHA: (14) implies:
% 6.11/1.62 | | (15) ~ (all_28_0 = all_16_1)
% 6.11/1.62 | | (16) addition(all_16_1, all_16_1) = all_28_0
% 6.11/1.62 | |
% 6.11/1.62 | | GROUND_INST: instantiating (additive_idempotence) with all_16_1, all_28_0,
% 6.11/1.62 | | simplifying with (9), (16) gives:
% 6.11/1.62 | | (17) all_28_0 = all_16_1
% 6.11/1.62 | |
% 6.11/1.62 | | REDUCE: (15), (17) imply:
% 6.11/1.63 | | (18) $false
% 6.11/1.63 | |
% 6.11/1.63 | | CLOSE: (18) is inconsistent.
% 6.11/1.63 | |
% 6.11/1.63 | End of split
% 6.11/1.63 |
% 6.11/1.63 End of proof
% 6.11/1.63 % SZS output end Proof for theBenchmark
% 6.11/1.63
% 6.11/1.63 1003ms
%------------------------------------------------------------------------------